On the distribution of ionospheric electron density observations

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For most space scientists, the general expectation of ionospheric measurements is that if properly binned, observations will obey a normal or Gaussian distribution. This paper challenges this assumption and argues that a lognormal distribution can better describe ionospheric densities. It presents a simple mathematical argument for ionospheric density observations obeying a lognormal distribution. To demonstrate the efficacy of the lognormal distribution, a sample distribution of total ion densities is presented and is compared with a lognormal distribution characterized by parameters estimated from the data. This distribution of DMSP observations fits a lognormal distribution with a probability plot correlation coefficient (PPCC) of 0.99932. The PPCC is the linear correlation between the ordered distribution and ordered statistical medians and measures how well a given set of values conforms to a given distribution. When the PPCC = 1, the distribution perfectly fits the data. When binned by solar activity (on the basis of the F10.7 cm proxy) and geomagnetic latitude, over 95.3% of the binned observations follow a lognormal distribution with a PPCC over 0.9. Since the topside electron densities tend to obey a lognormal distribution, the existing metrics for forecast performance need to be revised.