Articles | Volume 15, issue 23
https://doi.org/10.5194/amt-15-7039-2022
https://doi.org/10.5194/amt-15-7039-2022
Research article
 | 
07 Dec 2022
Research article |  | 07 Dec 2022

An improved formula for the complete data fusion

Simone Ceccherini, Nicola Zoppetti, and Bruno Carli

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Cited articles

Astoreca, R., Hurtmans, D., and Coheur, P.-F.: Fast Optimal Retrieval on Layers for IASI, Algorithm Theoretical Basis Document, The EUMETSAT Network of Satellite Application Facilities, 14 pp., https://acsaf.org/docs/atbd/Algorithm_Theoretical_Basis_Document_IASI_CO_Feb_2014.pdf (last access: 21 October 2022), 2014. 
Astoreca, R., Coheur, P., Hurtmans, D., Hadji-Lazaro, J., George, M., and Clerbaux, C.: Product User Manual, Near real-time IASI CO, The EUMETSAT Network of Satellite Application Facilities, 28 pp., https://www.eumetsat.int/media/41287 (last access 21 October 2022), 2017. 
Ceccherini, S.: Comment on “Synergetic use of IASI profile and TROPOMI total-column level 2 methane retrieval products” by Schneider et al. (2022), Atmos. Meas. Tech., 15, 4407–4410, https://doi.org/10.5194/amt-15-4407-2022, 2022. 
Ceccherini, S., Carli, B., and Raspollini, P.: Quality quantifier of indirect measurements, Opt. Express, 20, 5151–5167, 2012. 
Ceccherini, S., Carli, B., and Raspollini, P.: The average of atmospheric vertical profiles, Opt. Express, 22, 24808–14816, 2014. 
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Short summary
A new formula of the complete data fusion that, differently from the original one, does not contain matrices that can be singular is discussed. We show that the new formula is a generalization of the original one and analytically and numerically, using a real IASI ozone measurement, derive the errors made with the old formula when the generalized inverse of singular matrices is used. An operational version of the new formula that includes interpolation and coincidence errors is also provided.
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