The global atmospheric electric circuit could be important not only as a product of global thunderstorm activity (Bering et al., 1998) but also because it may cause climate change and weather itself via electrical effects on cloud microphysics, with external and internal drivers (Tinsley and Yu, 2004; Tinsley, 2008), which depend on the current density J_z flowing downwards from the ionosphere to the surface through clouds. This hypothesis has been reviewed in detail by Tinsley (2008).

The ionosphere forms a conducting shell, which is charged by highly electrified clouds, including thunderclouds in low latitude regions and air fronts at middle and high latitudes. The diurnal variations in the global upward current of approximately 1000 A create a diurnally varying ionospheric potential (Vi) that averages approximately 250 kV, which is essentially an equipotential out to approximately 50° geomagnetic latitudes. At any location away from the generators, the downward return current density (Jz) is 1–6 pA m-2, depending on the atmospheric resistance R of the column of the unit cross section there. The vertical column resistance R at any location is mainly determined by the altitude of the surface, the aerosol, the cloud and radioactive radon concentrations near the surface, and the flux of galactic cosmic rays (GCRs) at that latitude (Tinsley et al., 2006). The GCR flux creates ion pairs throughout the air column, increasing ion pairs cause the increase of conduct, leading to stronger Jz. There are two additional sources of ion pair production in the upper atmosphere: one is the relativistic electron flux and associated X-ray bremsstrahlung that penetrates down to approximately 30 km in sub-auroral latitudes (Tinsley, 1996; Frahm et al., 1997; Li et al., 2001a, b), and the other is solar energetic particle (SEP) events (Holzworth et al., 1987) that produce stratospheric ionization, excess positive charge, and occasionally a small amount of tropospheric ionization in the polar cap regions. We denote the stratospheric and tropospheric contributions to the column resistance at any location as S and T, respectively. Then Jz at that location is given by Ohm’s Law:   J z   =   V i   / ( T   +   S ) . Therefore, any input that modulates Vi, T, or S will also modulate Jz. There are several quasi-static numerical models to evaluate the global distribution of column resistance, such as Hays and Roble (1979), Makino and Ogawa (1985—herein M085), Sapkota and Varshneya (1990—herein SV90), Tinsley et al. (2006—herein TZ06), Zhou and Tinlsey (2010—herein ZT09), and there are comprehensive models with the whole atmospheric dynamics and chemical components to calculate the column resistance to provide a full description of the response of the global air conductivity to internal drivers (tropospheric and stratospheric aerosols, radon gas concentrations, clouds) and external drivers (galactic cosmic rays, comet aerosols, clouds), such as Baumgaertner et al. (2013—herein BTNL 2013) and Lucas et al. (2015—herein LBT 2015).

It was proposed that the reduction in Jz due to the Forbush decrease in GCRs could be attributed to the latitudinal variations in the low atmospheric dynamics, represented by the vorticity area index (VAI), and the amplitude of the response was proportional to the amplitude of the Forbush decrease (Tinsley and Deen, 1991). Other studies claimed that the relationship between Jz and VAI was due to the internal variation of the thunderstorm (Hebert et al., 2012) or interplanetary magnetic field (IMF) (Wilcox et al., 1973; Lam and Tinsley, 2016; Zhou et al., 2018). Responses of cloud cover to heliospheric current sheet (HCS) crossings have been found by Kniveton et al. (2008) and to Forbush decreases by Veretenenko and Pudovkin (1997), and responses of global cloud cover to global Jz changes inferred from the electric field (Ez) measurements at Vostok have been found by Kniveton et al. (2008). On longer time scales, the relation between the relativistic electron flux and the pressure fluctuation in the winter ice island pressure center is important (Zhou et al., 2014). These responses between space weather and atmospheric parameters were more significant two or three years after large volcanic eruptions, such as the eruption of Mt. Aguge, Mt. El Chikon, and Mt. Pinatubo, which was proposed to be due to additional resistance by the ultrafine aerosol layer in the stratosphere (Tinsley and Yu, 2004; Zhou et al., 2014). It has been suggested that after a large volcanic eruption, the gaseous H₂SO₄ in the descending branch of the Brewer-Dobson circulation could be condensed by ion media nucleation and form large concentrations of ultrafine aerosols with radii of a few nanometers or tens of nanometers at mid-high latitudes, which could significantly increase the column resistance in the stratosphere.

The initial evaluation of this effect was performed by the global circuit model of TZ06 (Tinsley et al., 2006). In the TZ06 model, an ultrafine aerosol layer was modeled by Tinsley et al. (2006), where column resistance is mainly shown in situations with and without the estimated stratospheric ultrafine volcanic aerosol layer. The layer is located poleward of ±40° geographic latitudes, where the layer column resistance becomes the dominant part of the stratosphere and is calculated for the absence of ionization due to electron precipitation, such as relativistic electron flux. This ionization is considered to be present most of the time and to make the ultrafine layer a good conductor so that the column resistance in the stratosphere (S) is negligible with respect to that in the troposphere (T). It is only for periods of a few days when the slow solar wind at the HCS crosses the earth that the precipitating relativistic electron flux decreases by an order of magnitude; R increases and Jz decreases at higher latitudes during a few years following large explosive volcanic eruptions. The concentration and spatial distribution of stratospheric ultrafine aerosols in TZ06 are artificial and static with no temporal variation, which provides only a rough estimation of their effects. The improved comprehensive model of BTNL 2013, based on CESM1, where the sulfate aerosol process in the stratosphere is from English et al. (2011), includes all types of aerosols, including ultrafine aerosols due to ion media nucleation in the stratosphere, and provides a more realistic picture of the global circuit. However, the lack of heating as aerosol radiative feedback in English et al. (2011) causes a large bias in the aerosol burden between simulations and observations. The improved aerosol-chemistry-climate model SOCOL-AERv2 by Feinberg et al. (2019) can already provide a more accurate treatment of stratosphere aerosols for low and high volcanic periods with aerosol radiative heating, sedimentation schemes, and coagulation efficiency. The purpose of this work is to investigate the effect of the stratospheric aerosol layer on the column resistance with the comprehensive global electric circuit model, which is based on SOCOL-AERv2 coupled with the global electric model of TZ06, where ultrafine aerosols due to ion media nucleation are involved to more accurately evaluate the effect of ultrafine aerosols and the temporal variation in this effect. In addition, the effects of ionization due to galactic cosmic rays and high-energy electron precipitation are addressed.

The chemistry-climate model (CCM) SOCOL (SOlar Climate Ozone Links) version three is a three-dimensional model developed by the research group at the Physical-Meteorological Observatory and World Radiation Center (PMOD/WRC) in collaboration with the Institute for Atmospheric and Climate Science, ETHZ Switzerland (Stenke et al., 2013). The effects of external drivers, such as galactic cosmic rays and solar protons, on the ozone layer and climate were investigated by the SOCOL model (Egorova et al., 2011; Mironova et al., 2021). A detailed description of the model can be found in Rozanov et al. (1999).

SOCOL is developed based on the Middle Atmosphere version of the European Center/Hamburg Model version 5 (MA-ECHAM5). MA-ECHAM5 (Roeckner et al., 2003) is the dynamical core of the model responsible for atmospheric physics and dynamics in SOCOL, with a hybrid sigma-pressure coordinate system spanning from the surface to 0.01 hPa. The horizontal spatial resolution of the model in this work is 3.75 × 3.75°. The model has 39 vertical levels from the surface to a height of approximately 80 km in a hybrid sigma-pressure coordinate system, and the vertical resolution decreases with altitude and is 2 km in the stratosphere. The dynamic frame in the model is solved with a semi-implicit time stepping scheme with a time resolution of 15 min. The advection of water vapor, cloud water, and trace constituents is calculated by a flux-based 25 mass-conserving and shape-preserving transport scheme (Lin and Rood, 1996). Full radiation calculations, chemistry, and transport calculations are performed every 2 h. The shortwave radiation scheme is based on the ECMWF model (Morcrette, 1991) with a modified parameterization for the water vapor continuum and corrected spectral Voigt line shape considering Doppler broadening at low pressure as well as with added aerosols, greenhouse gases, and clouds (Roeckner, 1995). The longwave radiation is based on the Rapid Radiative Transfer Model (RRTM) scheme (Mlawer et al., 1997).

The chemistry-transport module Model for the Evaluation of OZONe Trends (MEZON) (Egorova et al., 2003) shares the MA-ECHAM5 horizontal and vertical grids and treats 41 atmospheric species of hydrogen, oxygen, nitrogen, carbon, chlorine, and bromine groups treated with 140 gas-phase reactions, 46 photolysis reactions, and 16 heterogeneous reactions in/on liquid sulfate aerosols, water ice, and nitric acid trihydrate (NAT) (Stenke et al., 2013).

The ion pair production rate due to galactic cosmic rays is calculated by the CRAC (Cosmic Ray Atmospheric Cascade) model (Usoskin et al., 2010), which is based on a Monte Carlo simulation of the atmospheric cascade; in the troposphere and stratosphere, the accuracy is within 10% compared to the observation results. In the present work, we also add the ion pair due to low- and middle-energy electron precipitation (herein EEP, including LEE and MEE). The semi-empirical parameterization for LEE suggested by Funke et al. (2016) is involved, and the ionization rate due to MEE is based on Fang et al. (2010).

In the troposphere, 13 types of aerosols based on the GADS database and Hess et al. (1998) are involved, which is the same as the treatment in the TZ06 model. We use an analytical expression for the tropospheric aerosol size distribution given by Hess et al. (1998).

For the sulfate aerosol in the model, instead of the rough estimation that was used in TZ06, a detailed 2D sulfate aerosol model is coupled based on the updated size-resolved AER sulfate aerosol model, which was established in SOCOL by Sheng et al. (2015), Sukhodolov et al. (2018), and Feinberg et al. (2019). In this sulfate aerosol model, the particle distribution is resolved by 40 size bins spanning wet radii from 0.39 nm to 3.2 µm by volume doubling, which also provides the size distribution of the sulfate aerosol. In addition, the microphysical processes of homogeneous nucleation, condensation/evaporation, coagulation, and sedimentation, which were suggested by Sheng et al. (2015), are also included. In the upper stratosphere at altitudes over 30 km, the coagulation rate due to ion media nucleation is addressed in this new model, which is based on the INM model suggested by Yu and Turco (2001).

The column resistance (R) varies with latitude and longitude, and with the upper boundary of 60 km in our model, R is given by R = ∫ Zs 60 d z σ ( z ) (1) where Zs is the elevation of the surface and σ(z) is air conductivity. The current density J_z throughout the column is then J z = V i R (2) where V_i is the overhead ionospheric potential. The most complex problem for this global circuit model is in evaluating σ(z) globally as a function of altitude, latitude, longitude, and time.

In this model, the first step is the evaluation of the ion pair production rate; the next step is the evaluation of the aerosol particle concentrations. Then, using the approximation that the concentrations of positive and negative ions in the air are equal, the ion pair concentration (n) is obtained by solving the equation d N d t = q − α N 2 − ∑ ​ i β i S i N (3) for the steady state condition where dN/dt = 0, where t is the time. Then, the conductivity is given by σ = N e ( μ 1 + μ 2 ) (4) where e is the elementary charge, and μ 1 and μ 2 are the ion mobilities of the positive and negative ions.

We use a set of expressions for α that closely fit the results of Bates (1982). The expression for β_r as a function of aerosol particle radius, r, that we use is given by Hoppel (1985).

The present global electric circuit model calculates the atmospheric resistivity from the surface up to 60 km height with 335 bins. We took only 32 vertical bins below 60 km in the SOCOL-AERv2 model, all the outputs from the SOCOL-AERv2 model are linearly interpolated, and the sulfate gas concentration and sulfate aerosol surface area index (surface area density, SAD) are interpolated with the e power function.

Although the contribution of atmospheric resistivity from the sulfate aerosol layer in the lower stratosphere, called the Junge layer, is larger in the present simulation than in the previous TZ06 model (Tinsley et al., 2006), the aerosols in the upper stratosphere still seem to have a main effect on the column resistance at high latitudes. The ultrafine aerosol layer has a significant effect on the column resistance after the volcanic eruption. Tinsley (2005) claimed that there was an ultrafine aerosol layer in the upper stratosphere formed by ion media nucleation, as suggested by Yu and Turco (2001), which could be consistent with the unexplained variability on all time scales in measured stratospheric conductivity (Tinsley, 2005; Bering et al., 2005), especially in the descending branch of the Brewer-Dobson circulation at high latitudes. In the GEC model of the TZ06 model, the artificial ultrafine aerosol layer centered at 40 km was modeled based on the numerical simulation by Yu and Turco (2001) for an H₂SO₄ mass concentration of 6.35 × 10² μg m⁻³, which corresponds to a mass mixing ratio of 16 ppbm for the liquid droplets. In the TZ06 model, the sensitivity simulation showed that in the high volcanic eruption period, the column resistance in the high geomagnetic latitude region would be more sensitive to fluctuations in GCRs than in the low volcanic eruption period by a factor of two times due to the attribution of ultrafine aerosols and the high sensitivity of the polar region (Tinsley et al., 2006). Tinsley (2008) expected that the ultrafine aerosol concentration would have a maximum effect on the column resistance two years after a large volcanic eruption. However, in the present simulation, based on the chemical-climate model, the SAD in the ultrafine sulfate aerosol layer first appears in the descending branch of the Brewer-Dobson circulation at high latitudes soon after the eruption of Mt. Pinatubo, which significantly affects the regional column resistance. Different from previous models (TZ06, Tinsley et al., 2006), the column resistance response to volcanic eruptions shows a significant asymmetric structure in different hemispheres, and the column resistance in the high latitudes of the Northern Hemisphere has a larger response than that of the Southern Hemisphere. Two years after the volcanic eruption, the effect of ultrafine aerosols appears in only the North Atlantic region. This asymmetric structure might explain why more significant connections on day-to-day or annual time scales between space weather events and tropospheric responses, such as dynamic responses (Lam et al., 2014), cloud cover (Voiculescu et al., 2013) and cloud radiation (Frederick et al., 2019), appeared in the Northern Hemisphere than in the Southern Hemisphere.

It has been claimed that the Brewer-Dobson circulation is strengthened in the winter hemisphere (Butchart, 2014). Then, in the winter hemisphere, the transport rate of sulfate in the stratosphere is accelerated, and more ultrafine aerosols can be produced, which causes higher column resistance in the high latitude region of the winter hemisphere than in that of the summer hemisphere. In previous work, the main seasonal variation in the column resistance was mainly due to variations in the aerosol concentration in the troposphere due to changes in the boundary layer or emissions (Tinsley et al., 2006).

Many studies based on satellite observations and weather monitoring data have shown a significant connection between the fluctuations of space particles, such as GCRs, EEP, relativistic electron precipitation (REP), and the troposphere. The hypothesis suggested by Tinsley (2008) claimed that the return atmosphere current density (Jz) from the ionosphere to the land surface, which is partly controlled by atmospheric column resistance, could significantly affect the dynamic and thermal character in the troposphere through cloud electric microphysics, called the electri-scavenging or electri-anti-scavenging effect. The shorting out of the resistance of the ultrafine layer appears to be essentially when it occurs with REP, which produces bremsstrahlung X-rays that can dominate ion pair production in the middle stratosphere (Frahm et al., 1997). On the basis of SAMPEX measurements, this is likely to be most of the time at sub-auroral latitudes (Li et al., 2001a; Li et al., 2001b). However, for a few days around the times of HCS crossings, the REP decreases by up to an order of magnitude (Tinsley et al., 2000; Kirkland et al., 1996; Kniveton and Tinsley, 2004). Then, the column resistance in the sub-auroral region could increase to a high value, as calculated for the high volcanic aerosol situation, and Jz would decrease. This scenario for a decrease in Jz around the times of HCS crossings, when there is a high concentration of stratospheric aerosols, is in accordance with the sparse and noisy Jz observations for those times (Reiter, 1977; Fischer and Miihelisen, 1980; Tinsley et al., 1994). Because of the lack of a detailed model to simulate the global ion production rate due to REP, the effect of EEP is considered in the present model. The treatment of ultrafine aerosol concentrations and stratospheric ion mobility in the model confirms the essential contribution of ultrafine aerosols to column resistance. Even two years after a large volcanic eruption, the column resistance could still be sensitive to fluctuations in electron precipitation.

When the EEP effect was coupled with the seasonal effect, it could be predicted that the column resistance would be more sensitive to EEP changes in the winter hemisphere, which is consistent with most of the data analysis results.

Clouds seems to play an important role in local column resistance. The ZT09 model claimed that the variation in clouds caused less than 10% of the global atmospheric resistance, while the BTNL2013 model claimed that the effect of clouds was underestimated by the ZT09 model. Clouds are also a highly variable factor in atmospheric systems, in addition to total cloud coverage and cloud microphysics. While clouds are unstable and most cloud effects appear at low and middle latitudes, in high latitudes, ultrafine aerosols seem to be more important. Therefore, in the next step of the global circuit model, involving accurate clouds could be an important direction.

An updated global circuit model based on a chemistry-climate model (SOCOL-AERv2) with an accurate aerosol formation process is set up. The results provide a more accurate evaluation of the layer of ultrafine aerosols on global column resistance. The asymmetric distribution of ultrafine aerosols causes different responses of local column resistance to fluctuations in energetic particle precipitation. Column resistance in the high latitudes of the winter hemisphere would be more sensitive to energetic particle precipitation than that of the summer hemisphere. Since the EEP flux could contribute more relativistic electrons in the middle stratosphere, with the apparent ultrafine aerosol layer, the column resistance in the winter hemisphere would be more sensitive to fluctuations in the flux of REP. The whole atmosphere chemistry-climate model coupled with the global circuit sub-model including accurate ion pair production by REP could provide a clearer picture of the link between space weather and the troposphere.