| The Empirical Orthogonal Function (EOF)
retrieval technique consists of calculating
the eigenvectors of the spectra to later perform
a linear regression between these and the atmospheric
states, this first step is known as training.
At a later stage, known as performing the retrievals,
atmospheric profiles are derived
from measured atmospheric radiances.
When EOF retrievals are trained with a statistically
different data set than the one used for retrievals
two basic problems arise: significant biases appear in the retrievals
and differences between the covariances
of the training data set and the measured data set
degrade them.
The retrieved profiles will show
a bias with respect to the real profiles
which comes from the combined effect of the
mean difference between the training and the real spectra projected
into the atmospheric state space and the mean difference
between the training and the atmospheric profiles.
The standard deviations of the difference between the retrieved profiles
and the real ones show different behavior depending on whether
the covariance of the training spectra is bigger, equal or smaller
than the covariance of the measured spectra with which the
retrievals are performed.
The procedure to correct
for these effects is shown both analytically
and with a measured example. It consists of first calculating
the average and standard deviation of the difference between
real observed spectra and the calculated spectra obtained
from the real atmospheric state and the radiative transfer model
used to create the training spectra. In a later step,
measured spectra must be bias corrected with this average
before performing the retrievals
and the linear regression of the training must be performed
adding noise to the spectra corresponding to the aforementioned
calculated standard deviation.
This procedure is optimal in the sense that to improve the retrievals
one must resort to using a different training data set or a
different algorithm. |