Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends

TL;DR

This paper introduces new methods for estimating and testing correlations in spatially indexed functional data, with applications to ionospheric and magnetic field trend analysis, confirming a long-standing space physics hypothesis.

Contribution

It develops novel estimation techniques for spatial functional data and a significance test for their correlation, validated through simulations and real-world application.

Findings

Confirmed correlation between ionospheric trends and Earth's magnetic field changes

Demonstrated importance of accounting for spatial dependence in functional data analysis

Provided conclusive evidence supporting a space physics conjecture

Abstract

We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations $\mathbf{s}_1,\mathbf{s}_2,...,\mathbf{s}_N$. We propose several methods, and evaluate them by means of a simulation study. Next, we develop a significance test for the correlation of two such functional spatial fields. After validating the finite sample performance of this test by means of a simulation study, we apply it to determine if there is correlation between long-term trends in the so-called critical ionospheric frequency and decadal changes in the direction of the internal magnetic field of the Earth. The test provides conclusive evidence for correlation, thus solving a long-standing space physics conjecture. This conclusion is not apparent if the spatial dependence of the curves is neglected.