“…These terms are then used in the following equation, which defines a spatial variance, used as the SNO spatial sampling uncertainty:
where σ is the standard deviation of the sounder measurements within the big circle. This equation is derived such that the mean measurement over the big circle for each instrument is thought of as an area weighting of samples which overlap and samples which do not overlap (Taylor et al.,
2020). Note that if there is no overlap, the equation gives the expected sum of the uncertainty variance for two independent random variables, and if all of the footprints overlap, there is no sampling error.…”