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

Harmonized dataset of ozone profiles from satellite limb and occultation measurements

“…This assumption is appropriate for nearly all HARMOZ pairs due to the properties of data and the method for selecting the collocated measurement. For MIPAS-SCIAMACHY collocations, deviations from assumption are possible; this problem is discussed in Toohey and von Clarmann (2013). The bias is evaluated over the common altitude range of the pair of instruments, using concentration profiles.…”

Merged SAGE II, Ozone_cci and OMPS ozone profile dataset and evaluation of ozone trends in the stratosphere

“…Equation (2) is valid for random samples of uncorrelated data. As shown by Toohey and von Clarmann (2013), some deviations of the real standard error of the mean from that calculated using Eq. (2) can be observed for satellite observations.…”

Comparison of the CMAM30 data set with ACE-FTS and OSIRIS: polar regions

“…Here, we will compare coincident profiles from the satellites and the CMAM30 data set to establish the reliability of the model over the satellite period by looking at the median biases and median deviation about the biases. Essentially, the CMAM30 data is subsampled in approximately the same way that the satellite instruments "see" the atmosphere, avoiding errors due to differences between using the full model grid and the subsampling of the atmosphere by the satellite instruments (see Toohey and von Clarmann, 2013, for more details). Special attention will be given to regions and time periods where the model bias is greater, to examine possible causes for the discrepancies.…”