Evaluation of the cooling trend in the ionosphere using functional regression with incomplete curves

Abstract

We develop a statistical framework to test the hypothesis of the existence of an ionospheric cooling trend related to the global warming hypothesis; both are attributed to the same driver, namely the increased concentration of greenhouse gases. However, the study of a temporal trend in the ionosphere is easier because there are fewer covariates to be taken into account. The hypothesis that a cooling trend in the ionosphere exists has been an important focus of space physics research for over two decades. A central difficulty in reaching broadly agreed—on conclusions has been the absence of data with sufficiently long temporal and sufficiently broad spatial coverage. Complete time series of data that cover several decades exist only in a few separated (in-dustrialized) regions. The space physics community has struggled to combine the information contained in these data, and often contradictory conclusions have been reported based on the analyses relying on one or a few locations. We present a statistical analysis that uses all data, even those with incomplete temporal coverage. It is based on a new functional regression approach that can handle spatially indexed curves whose temporal domain depends on location and may contain gaps. The test statistic combines spatial and temporal dependence in the data and is approximately normally distributed. We conclude that a statistically significant cooling trend exists in the Northern Hemisphere. This confirms the hypothesis put forward in the space physics community over two decades ago.