Probability distributions of electron precipitation at high magnetic latitudes

We have integrated more than 600 million energetic electron spectra measured by the Special Sensor for Precipitating Particles, version 4 (SSJ4) sensor on nine Defense Meteorological Satellite Program (DMSP) spacecraft to obtain total number fluxes ( J tot [#/cm 2 s sr]) and energy fluxes ( JE tot [keV/cm 2 s sr]). These quantities were first separated into bins of 1° in magnetic latitude (MLat), 1 h in magnetic local time (MLT) and unit steps of Kp and then into 26 × 26 logarithmically‐spaced matrices covering the ranges 10 4 to 10 10.25 for JE tot and J tot and 10 −3 to 10 3.25 for average energy E AVE . Joint probability densities were then calculated as ratios of the number of samples within a matrix element to the total samples in each MLat‐MLT‐Kp bin. Our analysis shows that (1) in all bins probabilities for detecting any of the three parameters were lognormally distributed, and (2) in most bins distributions were multimodal. Measured multimodal probability distributions are well represented as superpositions of contributions from as many as four lognormal populations. These distributions have inherent positive skews with significant separations between their mean and most probable values. Average values of JE tot and E AVE now widely used to model distributions of auroral conductance at different levels of Kp are verified in the large DMSP data set. However, the lognormal and multimodal characters of their realizations in nature indicate that probabilities of detecting them at a given time in a MLat‐MLT‐Kp bin never exceed 10%.