Reconstruction of Total Suspended Matter data over the North Sea using DINEOF: use of the Gaussian anamorphosis transformation

Total Suspended Matter (TSM) from the SEVIRI sensor in the North Sea will be
analysed using DINEOF (Data INterpolating Empirical Orthogonal Functions), an EOFbased
technique to reconstruct missing data. The information needed to reconstruct the
missing data is computed internally based on a truncated EOF basis, so no assumptions
about the statistics of the data have to be made.
DINEOF uses the mean and covariance of the original data to calculate the EOF
basis. If the data are normally distributed, then the probability density distribution can
be completely described by their mean and the eigenvectors of the covariance matrix (the
EOFs). Variables such as TSM, however, do not have a Gaussian distribution, since TSM
is never smaller than zero. DINEOF typically does not take this into account. To overcome
this, a logarithmic transformation is usually performed to non-Gaussian variables,
although the exponential transformation needed to retrieve the original variable units after
using DINEOF leads sometimes to unrealistic high values in the reconstruction. An empirical
transformation, which allows to obtain a normally distributed variable based solely
on the data themselves, will be applied. This procedure, called Gaussian anamorphosis, is
sometimes used in data assimilation.
A Gaussian anamorphosis transformation will be applied to the TSM data of the
North Sea prior to their reconstruction. The high spatial and temporal dynamics of the gapfree
geostationary TSM data set will be analysed, focusing on tidal dynamics and sub-daily
variability.