Estimation of autocorrelation functions of atmospheric electric field variations using a Golomb array of sensors

Atmospheric electric filed (AEF) measured at the earthʼs 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 earthʼs 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.