Atmospheric electric filed (AEF) measured at the earth's surface varies in time and space in an irregular manner, which makes interpreting the results of such measurements a challenging task. Simultaneous measurements of the AEF using several sensors make it possible to study the spatiotemporal structure of AEF variations associated with local sources. In one dimension there is an optimal placement of sensors along a straight line with distances between them that are proportional to the divisions in the Golomb ruler such that, with a fixed number of sensors, there is a maximum possible number of different pairwise distances. An array of 7 electric field mills in a line and one more at a distance greater than the total length of the Golomb ruler was used to obtain simultaneous observational data set and estimate temporal and spatial autocorrelation functions of AEF variations in the range of distances 2.5-400 m and frequency range 10-3 - 1 Hz. In addition, to quantitatively describe and interpret the obtained dependences, the autocorrelation functions of the electric field created over a conducting plane by extended one-dimensional random Gaussian charge distribution with exponential autocorrelation function are analyzed. It is found that autocorrelation functions of observed and modeled electric field can be approximated by incomplete gamma functions with parameters depending on the height of charges and the correlation radius in charge distribution. The integral scales of AEF variations of local nature are examined depending on the same parameters, and the time integral scale is found to be inversely depends on the density of zeros of standardized time series of the AEF. The autocorrelation function of electric field created by charges, which are located at a distance from the earth's surface, much less than correlation radius in charge distribution, is the same as for the charges, and the rate of its decline decreases with increasing height of the system of charges.

The atmospheric boundary layer is the lowermost part of the atmosphere, the turbulent dynamics and electrodynamics of which are determined by the complex organization of processes in a dissipative environment with energy input from many sources. Regions of the atmosphere undisturbed by thunderstorms and precipitation are characterized by low-energy electrical processes, the study of which requires a developed instrument base and knowledge of the methods of synchronous spaced high-precision measurements of several physical quantities. This paper presents the results of recent studies of electricity of the atmospheric boundary layer of midlatitudes carried out using the measuring complex of Borok Geophysical Observatory of the Institute of Physics of the Earth, Russian Academy of Sciences (IPE RAS), and numerical modeling. Quantitative estimates of the average values and variability of small ion concentration, the corresponding components of electrical conductivity, and atmospheric electric field intensity are performed. Two types of electric structures formed by the electric current flow through a turbulent medium with inhomogeneous conductivity are defined.

We study analytically and numerically the relationships for a passive horizontal ring antenna, which is used as a collector for long-term observatory measurements of the atmospheric electric current density. The spatial distributions of the potential and the electric field as functions of the geometric characteristics of the antenna, which is located in a uniform atmospheric electric field, are determined in the electrostatic approximation and the parameters of the atmosphericion motion in the neighborhood of the antenna are calculated. The effective collecting area of the antenna is determined by two different methods. The time of deposition of the atmospheric ions with a given mobility on the collector as a function of the impact parameter and the initial height, which is determined by this parameter, is established. The results of direct measurements of the atmospheric electric current density by a collector are compared with the results of synchronous observations of the atmospheric electric field and the electrical conductivity in the surface layer.

We investigate the contribution of gamma radiation of natural radionuclides constituting the Earth crust, radioactive emanations, and their decay product in the ground to the rate of production of ion pairs in the atmosphere against the background of ionization of the atmosphere by radioactive gases exhaled to the atmosphere from the ground and propagating together with their short-lived daughter products. The radon flux density to the atmosphere is estimated by three methods: the reservoir method, the integration of altitude profiles of volume activity of radon, based on gamma spectroscopic observations and the diffusion model. The distribution of the gamma radiation dose from the earth radionuclides in the soil and the atmosphere is calculated using Gleant4 software. The propagation of the radon isotopes and their decay products in the atmosphere is calculated simulated using large eddy simulation supplemented with kinematic simulation of subgrid flux of a passive scalar. It is shown that depending on the specific activity of radionuclides in the ground, the soil parameters, and the turbulent regime of the atmosphere, the total contribution of gamma radiation to the ion pair production rate in the atmospheric boundary layer is approximately from 1 to 20% and increases upon a decrease in the penetrability of the upper ground layer for radioactive emanations.

The paper presents the results of the analytical and hardware development of a bipolar sensor for the concentration of small atmospheric ions, designed for long-term geophysical field observations. Theoretical estimates of the response function of the sensor are obtained. The dependence of the concentration of small atmospheric ions on the magnitude of the measured current of the aspiration capacitor and ion mobility spectrum is given. Numerical computations of the trajectories of small ions in an aspiration condenser of specified dimensions and geometry are performed. The probability of recording ions depending on their mobility is found. The circuit solutions and algorithms for the functioning of the hardware of the devices are described. Based on the development materials, prototypes of sensors are made. The technical characteristics and recommendations for the use of devices are given. Unlike analogues, the device is resistant to environmental influences. The sensors are tested in laboratory conditions and during the field observations of the electricity of the atmospheric boundary layer. In addition to being used as a part of a ground-based complex for geophysical observations, the developed sensor was used in an instrumental platform for balloon observations aloft. As a result of testing the devices, it was found that the functioning of the sensors is stable and the data are representative.

In this work, we study the space-time statistical features of variations in the atmospheric electric field (Ez) and space charge in the atmospheric boundary layer using a three-dimensional model and analysis of observational data. The model is a combination of large-eddy simulation supplemented with a subgrid kinematic model for scalar and the three-dimensional Poisson equation for the electric potential. Based on the calculated evolution of three-dimensional distributions of the space charge and electric potential, the variability of the spectral slopes of variations in the space charge, vertical potential difference, and the vertical component of the electric field Ez is investigated. The vertical profiles of Ez and the frequency power spectra of Ez variations at different heights computed are in reasonable agreement with the observed ones. It is shown that the cross-correlation of Ez at spatially separated points located on one straight line near the earth's surface decreases with increasing distance with a characteristic scale of a few tens meters and has a dependence on the angle between this line and the direction of the wind. Mean large-scale horizontal electric field defined through the position and amplitude of the potential extrema at the same height depends on height non-monotonically having a maximum value of about 5 V/m. Scaling exponents of structure functions for Ez variations are found to be significantly larger than those for space charge variations.

This paper reports the first investigations of the mid-latitude convective boundary layer (CBL) electricity above the homogeneous land surface using a large-eddy simulation (LES). Our approach uses LES together with a subgrid kinematic model for relative dispersion of scalar to calculate Lagrangian trajectories of notional particles carrying radioactive nuclei, small atmospheric ions, and charged aerosol particles. This technique opens up new possibilities for quantifying the influence of various environmental conditions on the formation of the electrical state of the undisturbed lower atmosphere. We examine the altitude distribution of principal atmospheric electrical quantities in the CBL and lower free weakly stable atmosphere without clouds depending on surface turbulent heat flux, geostrophic wind speed, mixed-layer height, ionospheric potential, and various ion production rates due to cosmic rays and radioactive gases.

In this study, we used a tethered balloon equipped with an instrumented platform to examine the altitude distribution of principal quantities of the lowest atmospheric region of the global electric circuit (GEC), radon volumetric activity, and aerosol particles concentration. Altitude soundings covered approximately 0.5 km of the lowest atmosphere and were accompanied by simultaneous ground-based measurements. This method of spaced observations allowed us to analyze the spatial and temporal changes in electrical quantities of the atmospheric boundary layer (ABL) more deeply than was possible before. Using successive balloon ascents and descents as well as holding the platform at certain heights, long-lived space charge layers were discovered and the rate of change of charge in atmospheric columns of various thickness was estimated. A charge density of small ions was determined to be enclosed in a range from -20 pC m(-3) to 30 pC m(-3) reaching the highest values with rare exceptions directly at the earth's surface. It was found that the electric field vertical profiles tend a decrease during the day most pronounced in the lower 100 m. Similar behavior is also demonstrated by radon and aerosol particle concentration profiles. Based on the results of soundings, columnar electrical resistance, electric potential, and electromotive force acting in the ABL in fair-weather conditions are quantified. These estimates show the significant contribution of the ABL to the GEC, which must be taken into account when considering it.

Complex tethered balloon observations aimed to investigate of mid-latitude atmospheric boundary layer (ABL) electricity including simultaneous measurement of spectral distribution of aerosol particles, radon activity, polar electrical conductivities and atmospheric electric field were conducted in the summer-autumn seasons 2016 and 2017. It is found that vertical profiles of polar electrical conductivities are largely determined by temperature stratification and stability of the ABL. Balloon observations on fixed altitude allowed registering a clear diurnal variation in aerosol concentration, radon activity, polar and total electrical conductivities related to diurnal variation of the ABL stability. Variability ranges for polar electrical conductivities ratio, space charge and atmospheric conduction current densities have been estimated. Results of numerical modeling of diurnal variation of radon activity, polar electrical conductivities and conduction current are presented and compared with the observed ones.

The atmospheric boundary layer considered a part of the planetary global electric circuit is known to exhibit a most dramatically changing in space and time atmospheric electrical variables. Extremely low specific electrical conductivity in the lower atmosphere is accompanied by the work of the electric generator associated with turbulent dynamo realizing itself through the space charge transport by boundary layer flows. The electromotive force of this generator acting in fair weather atmospheric regions provides a contribution to the global potential drop between the lower ionosphere and the earth's surface. In this study, the vertical electric current density produced by the turbulent transfer of space charge is investigated in the cases of the buoyancy-dominated and shear-dominated convective boundary layer (CBL) over the oceans based on second-order dissipation-conditioned Lagrangian stochastic model (LSM) applied near air-sea interface and conjugated with first-order LSM in the rest of the CBL. The total electric charge flux is treated in terms of mechanical transfer of atmospheric ions and charged aerosol particles by Lagrangian turbulence together with the drift of small ions in the self-consistent electric field. This approach based on a transported probability density function method offers persuasive advantages for quantitative estimates of local perturbations in the fair-weather electric field created by the atmospheric space charge carried by turbulent flows. It is found that the space charge density vertical profile only slightly depends on turbulence everywhere except for the wavy boundary layer about 10 m thick, a new parameterization of space charge vertical profile is proposed. Based on the simulation results, it can be predicted that in the buoyancy-dominated CBLs the electric field must be greater than in the sheared CBLs with other things being equal. Turbulent electromotive force and changes in total downward atmospheric electric current density are quantified. Simulated vertical profiles of electrical conductivity, space charge, electric field, and turbulent current density reasonably well reproduce previously reported observation results.

Due to the chaotic motion of charged particles carried by turbulent eddies, electrical quantities in the atmospheric boundary layer (ABL) have short-term variability superimposed on long-term variability caused by sources from regional to global scales. In this study the influence of radon exhalation rate, aerosol distribution and turbulent transport efficiency on the variability of fair-weather atmospheric electricity is investigated via Lagrangian stochastic modelling. For the mid-latitude lower atmosphere undisturbed by precipitation, electrified clouds, or thunderstorms, the model is capable of reproducing the diurnal variation in atmospheric electrical parameters detected by ground-based measurements. Based on the analysis of field observations and numerical simulation it is found that the development of the convective boundary layer, accompanied by an increase in turbulent kinetic energy, forms the vertical distribution of radon and its decaying short-lived daughters to be approximately coincident with the barometric law for several eddy turnover times. In the daytime ABL the vertical distribution of atmospheric electrical conductivity tends to be uniform except within the surface layer, due to convective mixing of radon and its radioactive decay products. At the same time, a decrease in the conductivity near the ground is usually observed. This effect leads to an enhanced ground-level atmospheric electric field compared to that normally observed in the nocturnal stably-stratified boundary layer. The simulation showed that the variability of atmospheric electric field in the ABL associated with internal origins is significant in comparison to the variability related to changes in global parameters. It is suggested that vertical profiles of electrical quantities can serve as informative parameters on ABL turbulent dynamics and can even more broadly characterize the state of the environment.

The physical mechanisms determining the variability of the vertical profiles of electrical conductivity, space charge density, and electric field in the undisturbed midlatitude lower atmosphere are discussed. The influence of the global and local mesoscale processes on the variability of electrical conductivity and the main component of the atmospheric electric field is estimated. The sunrise effect is studied, estimates are obtained for the charge accumulation rate in the column of the lower atmosphere and the corresponding growth rate of the field strength close to the ground. It is shown that the increase in the average charge density is mainly due to the breakdown of the stable stratification of the atmospheric boundary layer and transformation of the vertical profile of electrical conductivity following the convective mixing of a radon and its daughter products.

The electric state of the near-surface atmosphere up to a height of 400 m is investigated using a tethered balloon with a measuring platform and a ground-based information-measuring complex of the Borok middle-latitude geophysical observatory. For the first time, measurements were taken simultaneously for vertical profiles of the atmospheric electric field, polar electrical conductivities, size distribution of aerosol particles, and the volume activity of radon, which have allowed estimating the average values and variability of the space charge density and conduction current in the atmosphere. The height dependence of the electric potential with respect to the Earth's surface and electrical resistance of the near-surface atmospheric column under different conditions of the temperature stratification is studied.