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Atmospheric Measurement Techniques An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/amt-2019-32
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/amt-2019-32
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 22 Feb 2019

Research article | 22 Feb 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Atmospheric Measurement Techniques (AMT).

The cost function of the data fusion process and its application

Simone Ceccherini, Nicola Zoppetti, Bruno Carli, Ugo Cortesi, Samuele Del Bianco, and Cecilia Tirelli Simone Ceccherini et al.
  • Istituto di Fisica Applicata “Nello Carrara” del Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy

Abstract. When the complete data fusion method is used to fuse inconsistent measurements, it is necessary to add to the measurement covariance matrix of each fusing profile a covariance matrix that takes into account the inconsistencies. A realistic estimate of these inconsistency covariance matrices is required for effectual fused products. We evaluate the possibility of assisting the estimate of the inconsistency covariance matrices using the value of the cost function minimized in the complete data fusion. The analytical expressions of expected value and variance of the cost function are derived. Modelling the inconsistency covariance matrix with one parameter, we determine the value of the parameter that makes the reduced cost function equal to its expected value and use the variance to assign an error to this determination. The quality of the inconsistency covariance matrix determined in this way is tested for simulated measurements of ozone profiles obtained in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. As expected, the method requires a sufficient statistics and poor results are obtained when a small numbers of profiles are being fused together, but very good results are obtained when the fusion involves a large number of profiles.

Simone Ceccherini et al.
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Simone Ceccherini et al.
Simone Ceccherini et al.
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Short summary
We have analytically calculated the expected value and the variance of the cost function that is minimized in the Complete Data Fusion and propose a procedure that uses these quantities to constrain the values of the inconsistency covariance matrices. These matrices have to be added to the error covariance matrices of the measurements in order to fuse measurements that are inconsistent because of different vertical grids, not perfect time and space coincidence and different forward model errors.
We have analytically calculated the expected value and the variance of the cost function that is...
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