Testing the equality of mean functions of ionospheric critical frequency curves

This paper develops a significance test for evaluating the equality of the mean functions in two samples of spatially indexed functional data. The problem is motivated by an important question in space physics research which is related to the hypothesis of ionospheric global cooling (as opposed to the conjectured global warming of near surface atmosphere). The critical electron frequency of the ionosphere’s F2 region, foF2, can be used to empirically test conjectures about the trends in the ionosphere. We apply the proposed test to the foF2 records over eastern and western Europe to verify if there exists a conjectured difference between first order behavior of these records over regions with different magnetic inclinations. It is found that the difference between the means is statistically significant for night time records. The implications of this result are discussed. Finite sample performance of the proposed test is validated via numerical simulations.