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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 O<sub>3</sub> 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

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