Equivalence of data fusion and simultaneous retrieval.

A new method for the data fusion of atmospheric vertical profiles, referred to as complete fusion, is presented. Using the measurements of the MIPAS instrument, the performance of the method is compared with those of weighted and arithmetic means. The complete fusion perfectly reproduces the results of the simultaneous retrieval with equal error estimates and number of degrees of freedom, while arithmetic and weighted means have relatively low vertical resolution and differ from the simultaneous retrieval by more than their errors.

The average of atmospheric vertical profiles.

A new method to perform averages of atmospheric vertical profiles is presented. The method allows changing a-posteriori the strength of the constraint used in the retrievals of the single profiles with the purpose of optimizing the trade-off between measurement error and vertical resolution. The method is used to calculate averages of HCFC-22 profiles retrieved from MIPAS observations, demonstrating the possibility of correctly obtaining retrievals with smaller constraints (that is: having at least a factor ten greater errors) and more degrees of freedom by up to a factor two.

Quality quantifier of indirect measurements.

A quality quantifier, referred to as measurement quality quantifier (MQQ), is proposed for indirect measurements. It satisfies the property that the MQQ of the data fusion of two or more independent measurements is the sum of the MQQs of the individual measurements and can also be determined in absolute terms for ill-posed problems. It is calculated from the covariance and Jacobian matrices of the observations, but the same result is also obtained using the covariance and averaging kernel matrices of the retrieved quantities.

Rigorous determination of stratospheric water vapor trends from MIPAS observations.

The trend of stratospheric water vapor as a function of latitude is estimated by the MIPAS measurements by means of a new method that uses the measurement space solution. The method uses all the information provided by the observations avoiding the artifacts introduced by the a priori information and by the interpolation to different vertical grids. The analysis provides very precise values of the trends that, however, are limited by a relatively large systematic error induced by the radiometric calibration error of the instrument.

Optimal use of the information provided by indirect measurements of atmospheric vertical profiles.

A procedure for the optimal utilization and representation of the information retrieved from atmospheric observations is discussed. We show that the "measurement-space solution" exclusively contains the information present in the observations, but is not suitable for a representation of the retrieved profile in the form of a graph. The new method of the "null-space regularization", which provides in a complement space an external constraint and makes the solution compliant with this representation, is presented.

Use of apodization in quantitative spectroscopy.

Apodization, which is a tool frequently used for cosmetic representation and efficient modeling of a spectrum, is now also adopted in techniques for the quantitative retrieval of parameters from observed spectra. Whether apodization can help in quantitative spectroscopy is the subject of debate in the literature. We find that, when the considered spectral range is wide enough to accurately model the instrument line shape, the same results can be obtained with and without apodization of the spectrum.

Comparison of measurements made with two different instruments of the same atmospheric vertical profile.

The validation of atmospheric remote-sensing measurements involves the comparison of vertical profiles of atmospheric constituents obtained by different instruments. This operation is a complex one because it has to take into account the measurement errors that are described by the variance-covariance matrices and the different features of the two observing systems that are described by the averaging kernels. The procedure is discussed and a method of comparison that is rigorous and does not involve degradation of the available information is developed by use of the formalism of functional spaces.