Elimination of hidden a priori information from remotely sensed profile data T. von Clarmann and U. Grabowski Forschungszentrum Karlsruhe, Institut für Meteorologie und Klimaforschung, Karlsruhe, Germany
Abstract. Profiles of atmospheric state variables retrieved from
remote measurements often contain a priori information
which causes complication in the statistical use of data
and in the comparison with other measured or modeled data.
For such applications it often is desirable to remove the
a priori information from the data product. If the retrieval
involves an ill-posed inversion problem, formal removal of
the a priori information requires resampling of the data
on a coarser grid, which in some sense, however, is a prior
constraint in itself. The fact that the trace of the averaging
kernel matrix of a retrieval is equivalent to the number of degrees
of freedom of the retrieval is used to define an appropriate
information-centered representation of the data where each
data point represents one degree of freedom. Since regridding
implies further degradation of the data and thus causes
additional loss of information, a re-regularization scheme
has been developed which allows resampling without
additional loss of information. For a typical ClONO2
profile retrieved from spectra as measured by the Michelson
Interferometer for Passive Atmospheric Sounding (MIPAS),
the constrained retrieval has 9.7 degrees of freedom.
After application of the proposed transformation to a coarser
information-centered altitude grid, there are exactly 9 degrees
of freedom left, and the averaging kernel on the coarse grid is
unity. Pure resampling on the information-centered grid without
re-regularization would reduce the degrees of freedom to 7.1 (6.7)
for a staircase (triangular) representation scheme.
Citation: von Clarmann, T. and Grabowski, U.: Elimination of hidden a priori information from remotely sensed profile data, Atmos. Chem. Phys., 7, 397-408, doi:10.5194/acp-7-397-2007, 2007.