Abstract. Satellite remote sensing of methane (CH4) using the TROPOspheric Monitoring Instrument (TROPOMI) aboard the Copernicus Sentinel-5 Precursor (S5-P) satellite is key to monitor and quantify emissions globally. Overall, the S5-P methane data are of satisfying quality, demonstrated by the product validation with ground-based measurements from the Total Carbon Column Observing Network (TCCON). However, analysis of TROPOMI dry-air column mixing ratio (XCH4) data has pointed to a few false methane anomalies up to 20–40 ppb that can potentially be misinterpreted as enhancements due to strong emission sources. These artefacts are caused by spectral features of the underlying surfaces of specific materials (e.g. carbonate rocks), which are not well represented in the forward model of the retrieval algorithm. In this study we show that the observed anomalies are due to the surface model which describes the spectral dependence of the Lambertian albedo by a second-order polynomial in wavelength. By analysing the ECOSTRESS library that contains laboratory spectra for different types of surfaces, we find that a quadratic function might not be the most optimal representation of the surface reflectance spectral dependencies in the short-wave infrared (SWIR) range. Already the use of a third-order polynomial improves the methane data such that the anomalies disappear at several locations (e.g. Siberia, Australia and Algeria) without affecting the data quality elsewhere, and the quality of the fit significantly improves. We also found that the known bias in retrieved methane for low-albedo scenes slightly improves, but still, a posterior correction needs to be applied, leaving open the question about the root cause of the albedo bias. After applying the adjusted surface model globally, we perform the routine validation with TCCON and Greenhouse gases Observing SATellite (GOSAT) data. GOSAT comparison does not significantly improve, while TCCON validation results show a small improvement in some stations of 2–4 ppb, up to a factor of 10 smaller than the artificial XCH4 enhancements. This reflects that TCCON stations are not close to any of the corrected artefacts, hinting at a limitation of the current validation approach of the S5-P XCH4 data product.