Climatologies from satellite measurements: the impact of orbital sampling on the standard error of the mean

Abstract. Climatologies of atmospheric observations are often produced by binning measurements according to latitude and calculating zonal means. The uncertainty in these climatological means is characterised by the standard error of the mean (SEM). However, the usual estimator of the SEM, i.e., the sample standard deviation divided by the square root of the sample size, holds only for uncorrelated randomly sampled measurements. Measurements of the atmospheric state along a satellite orbit cannot always be considered as independent because (a) the time-space interval between two nearest observations is often smaller than the typical scale of variations in the atmospheric state, and (b) the regular time-space sampling pattern of a satellite instrument strongly deviates from random sampling. We have developed a numerical experiment where global chemical fields from a chemistry climate model are sampled according to real sampling patterns of satellite-borne instruments. As case studies, the model fields are sampled using sampling patterns of the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) and Atmospheric Chemistry Experiment Fourier-Transform Spectrometer (ACE-FTS) satellite instruments. Through an iterative subsampling technique, and by incorporating information on the random errors of the MIPAS and ACE-FTS measurements, we produce empirical estimates of the standard error of monthly mean zonal mean model O₃ in 5° latitude bins. We find that generally the classic SEM estimator is a conservative estimate of the SEM, i.e., the empirical SEM is often less than or approximately equal to the classic estimate. Exceptions occur only when natural variability is larger than the random measurement error, and specifically in instances where the zonal sampling distribution shows non-uniformity with a similar zonal structure as variations in the sampled field, leading to maximum sensitivity to arbitrary phase shifts between the sample distribution and sampled field. The occurrence of such instances is thus very sensitive to slight changes in the sampling distribution, and to the variations in the measured field. This study highlights the need for caution in the interpretation of the oft-used classically computed SEM, and outlines a relatively simple methodology that can be used to assess one component of the uncertainty in monthly mean zonal mean climatologies produced from measurements from satellite-borne instruments.