Not as trivial as one might think: the standard error of the mean

Usually the standard error of a climatological mean is calculated as the standard deviation divided by the square root of the number of observations. This standard recipe is, however, only valid for random samples of uncorrelated measurements. Regular measurements from a satellite orbit never are random, and atmospheric states at various locations are usually correlated. It could be shown that in the case of MIPAS monthly ozone climatologies, the standard formula typically overestimates the standard error of the mean. The figure shows the applicable correction factor, which is less than one for most cases.

A method has been developed by which the standard errors of the monthly means of satellite measurements are estimated on the basis of global fields provided by a model, which are sampled according to the satellite instrument's sampling pattern. For more information, see http://www.atmos-meas-tech.net/6/937/2013/amt-6-937-2013.pdf