The general method used for the derivation of HCHO VCDs from UV spectral measurements is the Differential Optical Absorption Spectroscopy method (DOAS; Platt and Stutz, 2008) which involves two main steps. First, the effective slant column amount (corresponding to the integrated HCHO concentration along the mean atmospheric optical path: Ns) is derived through a least-squares fit of the measured Earth reflectance spectrum by laboratory absorption cross-sections and a low order polynomial. Subsequently, a correction is applied to the slant column values to correct for appearing biases that may be of known or unknown origin. Finally, slant columns are converted into vertical columns by means of air mass factors (AMF) obtained from suitable radiative transfer calculations, accounting for the presence of clouds, surface properties, and best-guess HCHO vertical profiles.

In the UV, the sensitivity to HCHO concentrations in the boundary layer is intrinsically limited from space due to the combined effect of Rayleigh and Mie scattering that limits the radiation fraction scattered back toward the satellite. In addition, ozone absorption reduces the number of photons that reaches the lowest atmospheric layers. Furthermore, the absorption signatures of HCHO are weaker than those of other UV Vis absorbers, such as e.g. NO2. As a result, the retrieval of formaldehyde from space is noise sensitive and error prone. While the precision (or random error uncertainty) is driven by the signal to noise ratio of the recorded spectra and by the width of the retrieval interval, the trueness (or systematic error uncertainty) is limited by the current knowledge of the external parameters needed in the different retrieval steps.

The selection of the optimal retrieval interval must maximize the sensitivity of the inversion to the HCHO absorption signatures while minimizing errors from geophysical and instrument related spectral features. The retrieval interval should be chosen as wide as possible to maximize the number of sampling points while avoiding overlap with strong atmospheric spectral features from interfering species (mainly O3, BrO, and O4). The DOAS algorithm intrinsically assumes that the atmosphere is optically thin so that the optical light path is independent of wavelength within the fitting window. Hence the method is accurate only for modest ozone absorption (i.e., for small to medium solar zenith angles). Generally, the effect of ozone misfit on the retrieval can be handled by introducing wavelength dependent-AMF in the fit, and by applying appropriate background corrections on the columns. The correlation with BrO absorption can be reduced by using two different wavelength intervals to fit BrO and HCHO (see section 5.3: Formaldehyde slant column retrieval).

The Sentinel-5P sensor TROPOMI samples the Earth’s surface with a revisit time of one day and with an unprecedented spatial resolution of 7x3.5 km2 (5.5x3.5 km2 from 6 August 2019). Furthermore, the signal to noise ratio of TROPOMI is required to be equivalent to OMI in the UV-Visible range. This allows the resolution of fine details and S5P will arguably be a valuable tool to better study NMVOC emissions. Nevertheless, it poses additional constraints on the retrieval code for several reasons:
1. Computational speed: the Level 1b data flow delivers spectral measurements for band 3 with a size of 4 gigabytes per orbit (15 orbits daily).
2. Precision: given the required signal to noise ratio of measured spectra, the air quality requirements for HCHO [RD04] will not be met for individual ground pixels. Spatial and temporal averages of the HCHO columns will have to be considered in order to provide useful constraints on human and natural NMVOC emissions.
3. Trueness: currently, the spatial resolution of global-scale external parameters needed in the AMF calculation (e.g. albedo or a priori HCHO profiles) is much coarser than the resolution of TROPOMI. This introduces errors in the final vertical columns, mostly for coastal regions and localized sources (Heckel et al., 2011)

To fully exploit the potential of satellite data, applications relying on tropospheric HCHO observations require high quality long-term time series, provided with well characterized errors and averaging kernels, and consistently retrieved from the different sensors. Furthermore, as the HCHO observations are aimed to be used synergistically with other species observations (e.g. for air quality applications), it is essential to homogenize as far as possible the retrieval methods as well as the external databases, in order to minimize systematic biases between the observations.