  Network-based analyses of dynamical systems have become increasingly popular
in climate science. Here we address network construction from a statistical
perspective and highlight the often ignored fact that the calculated
correlation values are only empirical estimates. To measure spurious behaviour
as deviation from a ground truth network, we simulate time-dependent isotropic
random fields on the sphere and apply common network construction techniques.
We find several ways in which the uncertainty stemming from the estimation
procedure has major impact on network characteristics. When the data has
locally coherent correlation structure, spurious link bundle teleconnections
and spurious high-degree clusters have to be expected. Anisotropic estimation
variance can also induce severe biases into empirical networks. We validate our
findings with ERA5 reanalysis data. Moreover we explain why commonly applied
resampling procedures are inappropriate for significance evaluation and propose
a statistically more meaningful ensemble construction framework. By
communicating which difficulties arise in estimation from scarce data and by
presenting which design decisions increase robustness, we hope to contribute to
more reliable climate network construction in the future.
