A new quality analysis applied to MIPAS operational products

Recently a new quality quantifier, referred to as measurement quality quantifier (MQQ), has been introduced. It is derived from the Fisher information matrix and quantifies in absolute way the quality of the observations with respect to the retrieved parameters independently of any constraint that can be used in the retrieval. Differently from other information quantifiers, such as the Shannon information content, it can be also defined in absolute terms for ill-posed inverse problems. When the measured quantity is a continuous distribution (such as a vertical profile) the MQQ depends on the sampling grid of the distribution and the need arises of characterizing the observations independently of the selected grid. To this purpose the information distribution is derived from the MQQ and this quantity makes possible the comparison of quality of measurements represented on different grids as a function of altitude. The MQQ and the quantifiers derived from it provide an assessment of the information contained in the observations, but do not provide any information on how many independent components of the unknown profile have been measured. Therefore, in order to have a complete description of the measurement quality, we propose to complement the information provided by the quantifiers derived from the MQQ with the number of degrees of freedom (DOF) of the retrieval. The diagonal elements of the averaging kernel matrix are used to define the DOF distribution that determines the contribution to the number of DOF as a function of altitude. We use the information distribution and the DOF distribution to perform a quality assessment of the MIPAS operational products. As a consequence of the discontinuity occurred in the MIPAS measurements the operational MIPAS products consist in two sets of vertical profiles (obtained from full resolution (FR) and optimized resolution (OR) measurements) retrieved using different microwindows (MWs) from spectra acquired with different spectral resolutions and different limb-viewing scenarios. A further dataset will be derived from FR measurements and provided by ESA to the users. This will be obtained degrading their spectral resolution to that of the OR measurements and performing the retrieval with the same MWs as for the OR measurements. This third dataset, together with the profiles retrieved from OR measurements, should provide a more consistent dataset throughout the full mission for trend estimation. The quality analysis based on information and DOF distributions is applied to the three datasets of the MIPAS operational products showing that these quantifiers provide an useful tool for the comparison of the different operational choices. These quantifiers fully characterize as a function of altitude the information provided by the MIPAS products and can be used to assess the redundancies and the complementarities of these products with those of other experiments.