## 2 Materials and Methods
### Simulated HCHO Columns Using MAGRITTE and IMAGES CTMs  
Simulations of HCHO columns are performed using the Model of Atmospheric composition at Global and Regional scales using Inversion Techniques for Trace gas Emissions (MAGRITTE) v1.1, a global and regional three-dimensional chemistry-transport model (CTM) of the troposphere [86; 87]. Most model parameterizations are inherited from the global Intermediate Model of the Global and Annual Evolution of Species (IMAGESv2) model [46; 61; 88; 89; 90]. MAGRITTE calculates the concentrations of 182 chemical compounds in the troposphere with a spin-up time of six months. The horizontal resolution of the model is either 2\({}^{\circ}\) (latitude) \(\times\) 2.5\({}^{\circ}\) (longitude) at a global scale or 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) at a regional scale, while the vertical coordinate is a hybrid sigma-pressure system resolved in 40 unevenly spaced levels extending from the surface to the lower stratosphere (44 hPa). Meteorological fields are provided by European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalyses. The model calculates monthly averaged columns at the OMI overpass time (13:30), taking into account the sampling date statistics of the satellite. The chemical degradation mechanism of isoprene relies on the Leuven isoprene mechanism [11; 91] and the Caltech oxidation mechanism [92], accounting for relevant theoretical and laboratory studies. The bottom-up fluxes of HCHO precursors are prescribed as follows. The biomass burning inventory is obtained from the Global Fire Emission Database version 4 (GFED4s; [93]) on a daily basis ([[https://globalifredata.org](https://globalifredata.org)]([https://globalifredata.org](https://globalifredata.org)), accessed on 22 March 2013). The anthropogenic sources of non-methane VOC species are taken from the Emission Database for Global Atmospheric Research version 4.3.2 (EDGARv4.3.2, [94]) and the anthropogenic CO, NO\({}_{\rm x}\), OC, SO\({}_{2}\), BC and NH\({}_{3}\) are obtained from the Hemispheric Transport of Air Pollution version 2 (HTAPv2; [95]) database for 2010. Due to their limited availability, the EDGARv4.3.2 emissions are set constant at their 2012 values after this year. Both inventories are available at [[https://edgar.jrc.ce.europa.eu](https://edgar.jrc.ce.europa.eu)]([https://edgar.jrc.ce.europa.eu](https://edgar.jrc.ce.europa.eu)) (accessed on 28 August 2018). Over the U.S., the anthropogenic EDGAR emissions are scaled down to match emission estimates based on aircraft NOx concentrations and nitric acid deposition data, according to [96]. Biogenic emissions are prescribed as follows. As in [46], MEGAN-MOHYCAN global simulations provided fluxes of isoprene, monoterpene, and 2-methyl-3-buten-2-ol (MBO) using meteorological fields from ECMWF reanalysis (ERA-Interim; [97]) and gridded emission factors [5] based on detailed land cover description and species-specific emission factors. The global bottom-up inventory of biogenic isoprene emissions is publicly available from emissions.aeronomie.be/index.php/bottom-up/isoprenev2018 (accessed on 1 April 2022). Biogenic sources of ethylene, formaldehyde, and acetone, based on the MEGAN model are taken from the database of Emissions of atmospheric Compounds and Compilation of Ancillary Data (ECCAD, [[http://eccad.aeris-data.fr](http://eccad.aeris-data.fr)]([http://eccad.aeris-data.fr](http://eccad.aeris-data.fr)), accessed on 3 June 2019). Biogenic emissions of acetaldehyde and ethanol are parameterized as in [98]. Finally, the biogenic methanol emissions are provided by inverse modelling constrained by spaceborne methanol data [99].