  Spatial, amplitude and phase variations in spatial functional data are
confounded. Conclusions from the popular functional trace variogram, which
quantifies spatial variation, can be misleading when analysing misaligned
functional data with phase variation. To remedy this, we describe a framework
that extends amplitude-phase separation methods in functional data to the
spatial setting, with a view towards performing clustering and spatial
prediction. We propose a decomposition of the trace variogram into amplitude
and phase components and quantify how spatial correlations between functional
observations manifest in their respective amplitude and phase components. This
enables us to generate separate amplitude and phase clustering methods for
spatial functional data, and develop a novel spatial functional interpolant at
unobserved locations based on combining separate amplitude and phase
predictions. Through simulations and real data analyses, we found that the
proposed methods result in more accurate predictions and more interpretable
clustering results.
