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

[摘要] Climatologies of atmospheric observations are often produced bybinning measurements according to latitude and calculating zonalmeans. The uncertainty in these climatological means ischaracterised by the standard error of the mean (SEM). However, theusual estimator of the SEM, i.e., the sample standard deviationdivided by the square root of the sample size, holds only foruncorrelated randomly sampled measurements. Measurements of theatmospheric state along a satellite orbit cannot always beconsidered as independent because (a) the time-space intervalbetween two nearest observations is often smaller than the typicalscale of variations in the atmospheric state, and (b) the regulartime-space sampling pattern of a satellite instrument stronglydeviates from random sampling. We have developed a numerical experiment whereglobal chemical fields from a chemistry climate model are sampledaccording to real sampling patterns of satellite-borneinstruments. As case studies, the model fields are sampled using sampling patterns of the MichelsonInterferometer for Passive Atmospheric Sounding (MIPAS) andAtmospheric Chemistry Experiment Fourier-Transform Spectrometer(ACE-FTS) satellite instruments. Through an iterative subsamplingtechnique, and by incorporating information on the random errorsof the MIPAS and ACE-FTS measurements, we produce empirical estimates of thestandard error of monthly mean zonal mean model O₃ in5° latitude bins. We find that generally the classic SEMestimator is a conservative estimate of the SEM, i.e., the empiricalSEM is often less than or approximately equal to the classic estimate.Exceptions occur only when natural variability is larger thanthe random measurement error, and specifically ininstances where the zonal sampling distribution shows non-uniformitywith a similar zonal structure as variations in the sampled field,leading to maximum sensitivity to arbitrary phase shifts between thesample distribution and sampled field. The occurrence of suchinstances is thus very sensitive to slight changes in the samplingdistribution, and to the variations in the measured field. Thisstudy highlights the need for caution in the interpretation of theoft-used classically computed SEM, and outlines a relatively simplemethodology that can be used to assess one component of theuncertainty in monthly mean zonal mean climatologies produced frommeasurements from satellite-borne instruments.

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