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The Empirical Orthogonal Function (EOF)retrieval technique consists of calculatingthe eigenvectors of the spectra to later performa linear regression between these and the atmosphericstates, this first step is known as training.At a later stage, known as performing the retrievals,atmospheric profiles are derivedfrom measured atmospheric radiances.<P  style="line-height: 20px;">When EOF retrievals are trained with a statisticallydifferent data set than the one used for retrievalstwo basic problems arise: significant biases appear in the retrievalsand differences between the covariancesof the training data set and the measured data setdegrade them.<P  style="line-height: 20px;">The retrieved profiles will showa bias with respect to the real profileswhich comes from the combined effect of themean difference between the training and the real spectra projectedinto the atmospheric state space and the mean differencebetween the training and the atmospheric profiles.<P  style="line-height: 20px;">The standard deviations of the difference between the retrieved profilesand the real ones show different behavior depending on whetherthe covariance of the training spectra is bigger, equal or smallerthan the covariance of the measured spectra with which theretrievals are performed.<P  style="line-height: 20px;">The procedure to correctfor these effects is shown both analyticallyand with a measured example. It consists of first calculatingthe average and standard deviation of the difference betweenreal observed spectra and the calculated spectra obtainedfrom the real atmospheric state and the radiative transfer modelused to create the training spectra. In a later step,measured spectra must be bias corrected with this averagebefore performing the retrievalsand the linear regression of the training must be performedadding noise to the spectra corresponding to the aforementionedcalculated standard deviation.This procedure is optimal in the sense that to improve the retrievalsone must resort to using a different training data set or adifferent algorithm

atmospheric chemistry and physics

Technical note: analytical estimation of the optimal parameters for the EOF retrievals of the IASI Level 2 Product Processing Facility and its application using AIRS and ECMWF data