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 $X(mathbf{s}_k;t),tin[0,T],$ 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.
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