## 2 Materials and Methods
### Retrieval Algorithms  
#### 2.2.1 Round-Robin of MAX-DOAS Retrievals of NO\({}_{2}\), HCHO and Aerosols  
As part of the system design phase, an extensive assessment of the performance of retrieval algorithms for tropospheric trace gases and aerosols from MAX-DOAS measurements was performed to identify suitable retrieval algorithms for the FRM4 DOAS operational processor. This retrieval round-robin included the eight different algorithms listed in Table 2, of which five were based on optimal estimation methods (OEM [17]), two parameterised approaches using lookup tables and one algorithm was based on an analytical approach. Retrievals were performed for a variety of different synthetic profiles of NO\({}_{2}\), HCHO and aerosol profiles, allowing for a quantitative comparison of true and retrieved profiles. These scenarios included exponential profiles and box profiles of different heights, as well as uplifted layers and two cloud cases, yielding in total of 110 different combinations of trace gases and aerosol scenarios. For each scenario, a set of differential slant column densities (dSCDs) was simulated by each of the forward models of the participating retrieval algorithms for a viewing angle sequence consisting of ten elevation angles from 1\({}^{\circ}\) to 90\({}^{\circ}\). The median from all forward models then served as the reference dSCD dataset that represented the input for the retrieval algorithms. In addition to retrievals without any noise (dataset v1), retrievals with typical levels of artificial noise (dataset v1n) were also performed. Retrieval settings, including aerosol optical properties and the specifications of the layer grid, were prescribed. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & **Institute** & **Method** & **Reference** \\ \hline bePRO & BIRA-IASB & OEM & [18] \\ BOREAS & IUP Bremen & OEM & [19] \\ HEIPRO & IUP Heidelberg & OEM & [20] \\ MMF & BIRA-IASB & OEM & [21] \\ PRIAM & MPC & OEM & [22] \\ MAPA & MPIC & PAR & [23] \\ MARK & KNMI & PAR & [24] \\ NASA & NASA 1 & ANA & Black Software Suite Manual, version 1.8 2 \\ \hline \hline \end{tabular}  
* NASA-Goddard, Greenbelt, United States; 2 [[https://www.pandonia-global-network.org/home/documents/manuals/](https://www.pandonia-global-network.org/home/documents/manuals/)]([https://www.pandonia-global-network.org/home/documents/manuals/](https://www.pandonia-global-network.org/home/documents/manuals/)), accessed on 27 November 2024.  
\end{table} 
Table 2: MAX-DOAS retrieval algorithms participating in the retrieval round-robin. OEM: optimal estimation; PAR: parameterised retrieval based on lookup tables; ANA: analytical approach. Figure 1: Current geographical distribution of the UV–Visible instruments that are centrally processed by the FRM4 DOAS system (for more details, see Table 1). Since the results of this retrieval round-robin were already published [25], we present only a summary here. Results of the comparison of AODs and trace gas vertical column densities (VCDs) are shown in Figure 2. Generally, good agreement between true and retrieved aerosol and trace gas profiles was found for most of the models. Retrieved surface values of aerosol extinction and trace gas concentrations deviated from the truth by (0.08-0.25) km\({}^{-1}\) and (5.9-15.0) \(\times\) 10\({}^{10}\) molec cm\({}^{-3}\) (or about 2.4-6 ppb), respectively. The most suitable retrieval algorithms both in terms of computational performance and accuracy turned out to be the MMF algorithm based on optimal estimation as well as the MAPA algorithms based on a fast parameterised approach using lookup tables. It was therefore decided to implement these two algorithms into the FRM4 DOAS operational processor. This allows for a cross-validation of both algorithms on an operational basis. Furthermore, the validity of the retrieval products can be assessed based on the level of agreement of both algorithms. See [25] for a comprehensive description of the results of this retrieval round-robin, which also includes a discussion of uncertainties.