Statistical and functional representations of the pattern of auroral energy flux, number flux, and conductivity

<jats:p>The Hardy et al. (1985) global patterns of the integral energy flux and average energy of precipitating auroral electrons are used to determine the global pattern of the electron‐produced, height‐integrated Hall and Pedersen conductivities. The conductivities were determined in spatial bins in magnetic local time (MLT)‐corrected geomagnetic latitude (CGL) coordinates for all MLTs and for CGLs greater than 50° and for seven levels of activity as measured by <jats:italic>Kp</jats:italic>. The conductivities vary smoothly with latitude and MLT typically having a single peak in latitude within the auroral oval at any MLT. On the nightside the two conductivities increase with increasing <jats:italic>Kp</jats:italic>. The largest conductivities are found near midnight, where the peak value of the Pedersen (Hall) conductivity varies from 3.09 (4.05) mhos to 12.5 (25.9) mhos as <jats:italic>Kp</jats:italic> varies from 0 to ≥6−. The peak conductivity decreases with MLT away from midnight with the lowest peak values found postnoon. At noon and on much of the morning side of the oval the Pedersen and Hall conductivities increase for <jats:italic>Kp</jats:italic> up to 2 and then decrease for higher <jats:italic>Kp</jats:italic>. The highest ratios of the Hall to Pedersen conductivity are on the morning side of the oval and at noon. The peak conductivities on the dayside are significant compared to the conductivities produced by solar radiation at all seasons of the year. The global maps of the integral energy flux, integral number flux, and height‐integrated Hall and Pedersen conductivities at each level of <jats:italic>Kp</jats:italic> were fit using both spherical harmonic and Epstein functions. The Epstein functions were found to reproduce better the original maps. At <jats:italic>Kp</jats:italic> = 2 the distribution of differences between the Epstein function fit and the original data is roughly symmetric about zero with a full width at half maximum of 16 (20)% for the Pedersen (Hall) conductivity and 32 (40)% for the integral energy (number) flux. The distribution of differences broadens with increasing and decreasing activity.</jats:p>