The thermal infrared nadir spectra of IASI (Infrared Atmospheric Sounding Interferometer) are successfully used for retrievals of different atmospheric trace gas profiles. However, these retrievals offer generally reduced information about the lowermost tropospheric layer due to the lack of thermal contrast close to the surface. Spectra of scattered solar radiation observed in the near-infrared and/or shortwave infrared, for instance by TROPOMI (TROPOspheric Monitoring Instrument), offer higher sensitivity near the ground and are used for the retrieval of total-column-averaged mixing ratios of a variety of atmospheric trace gases. Here we present a method for the synergetic use of IASI profile and TROPOMI total-column level 2 retrieval products. Our method uses the output of the individual retrievals and consists of linear algebra a posteriori calculations (i.e. calculation after the individual retrievals). We show that this approach has strong theoretical similarities to applying the spectra of the different sensors together in a single retrieval procedure but with the substantial advantage of being applicable to data generated with different individual retrieval processors, of being very time efficient, and of directly benefiting from the high quality and most recent improvements of the individual retrieval processors. We demonstrate the method exemplarily for atmospheric methane (CH4). We perform a theoretical evaluation and show that the a posteriori combination method yields a total-column-averaged CH4 product (XCH4) that conserves the good sensitivity of the corresponding TROPOMI product while merging it with the high-quality upper troposphere-lower stratosphere (UTLS) CH4 partial-column information of the corresponding IASI product. As a consequence, the combined product offers additional sensitivity for the tropospheric CH4 partial column, which is not provided by the individual TROPOMI nor the individual IASI product. The theoretically predicted synergetic effect is verified by comparisons to CH4 reference data obtained from collocated XCH4 measurements at 14 globally distributed TCCON (Total Carbon Column Observing Network) stations, CH4 profile measurements made by 36 individual AirCore soundings, and tropospheric CH4 data derived from continuous ground-based in situ observations made at two nearby Global Atmospheric Watch (GAW) mountain stations. The comparisons clearly demonstrate that the combined product can reliably detect the actual variations of atmospheric XCH4, CH4 in the UTLS, and CH4 in the troposphere. A similar good reliability for the latter is not achievable by the individual TROPOMI and IASI products.