## 2 Materials and Methods
### Data Sourcing from Life Cycle Inventories and Complementary Materials

Table 1: _Cont._The different scenarios for which data was available are described in Table 2, with a brief description of the system and the source from which the data was sourced. \begin{table}
\begin{tabular}{c c c c} \hline
**Product** & **Scenario** & **System Description** & **Source** \\ \hline \multirow{6}{*}{Algae biomass} & 1 & Microalgae from wastewater with CO\({}_{2}\) injection & [36] \\ \cline{2-3}  & & & \begin{tabular}{c} Confidential industry data. \\ \end{tabular} \\ \cline{2-3}  & 2 & Microalgae from wastewater with CO\({}_{2}\) injection & Anonymized life cycle inventory is \\  & & and polyelectrolyte addition & Available in the Supplementary \\  & & & Material (Table S2). \\ \cline{2-3}  & 3 & Microalgae from wastewater with organic & [37] \\  & & flocculant & \\ \cline{2-3}  & 4 & Microalgae from biowaste & \begin{tabular}{c} Confidential industry data. \\ \end{tabular} \\  & & 4 & Microalgae from biowaste & Anonymized life cycle inventory is \\  & & & available in the Supplementary \\  & & & Material (Table S3). \\ \hline \multirow{6}{*}{Compost} & 1 & Food and green waste anaerobic digestion and \\  & & & electricity \\ \cline{2-3}  & 2 & \begin{tabular}{c} Food and green waste anaerobic digestion and \\ \end{tabular} \\  & 2 & \begin{tabular}{c} Food and green waste anaerobic digestion and \\ \end{tabular} \\  & 3 & \begin{tabular}{c} Food and green waste anaerobic digestion and \\ \end{tabular} \\  & 4 & \begin{tabular}{c} composting in central Europe, with in situ \\ electricity production from biogas \\ \end{tabular} \\ \cline{2-3}  & 5 & \begin{tabular}{c} Food and green waste anaerobic digestion and \\ \end{tabular} \\  & 5 & \begin{tabular}{c} composting in northern Europe, with grid \\ electricity \\ \end{tabular} \\ \cline{2-3}  & 6 & \begin{tabular}{c} Food and green waste anaerobic digestion and \\ \end{tabular} \\  & 6 & \begin{tabular}{c} Food and green waste anaerobic digestion and \\ \end{tabular} \\ \hline \multirow{6}{*}{Feather meal} & 1 & Feather meal production, from unspecified poultry & [26] \\ \cline{2-3}  & 2 & Feather meal production, from goose feathers & [26; 38; 39; 40] \\ \cline{2-3}  & 3 & \begin{tabular}{c} Feather meal production, from chicken layer \\ feathers \\ \end{tabular} \\ \hline \multirow{6}{*}{Wood vinegar} & 1 & \begin{tabular}{c} Wood vinegar from unspecified wood biomass. \\ Wood dust used to produce heat. Co-products \\ (NCG, biocrude oil and biochar) are outputs \\ \end{tabular} \\  & 2 & \
\begin{tabular}{c} Wood vinegar from unspecified wood biomass. \\ Wood dust disposed of as waste. Co-products \\ (NCG, biocrude oil and biochar) are outputs \\ \end{tabular} \\ \cline{2-3}  & 3 &
\begin{tabular}{c} Wood vinegar from unspecified wood biomass. \\ Wood dust, NCG and biocrude oil are used to \\ produce heat. Biochar and surplus biocrude oil are \\ outputs \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 2: Characterization of the different scenarios considered for the calculation of the circularity indicators. The LCIs of compost, feather meal, and spent mushroom substrate include a Data Quality Rating (DQR), assessed using the \"pedigree matrix\" developed by [PERSON] and [PERSON] [43]. This methodology assigns a score ranging from 1 (highest quality) to 5 (lowest quality), based on a rubric that evaluates five criteria: reliability, completeness, temporal correlation, geographical correlation, and further technological correlation. The resulting DQR scores for these three products are as follows: compost, 2.27; feather meal, 2.22; and spent mushroom substrate, 2.02 [44]. According to the Product Environmental Footprint (PEF) method [45], these values reflect data quality levels ranging between \"good\" and \"very good\". Regarding the data quality of the LCIs for algae biomass, [PERSON] et al. [29; 30] reported an inventory consisting of 29 flows, of which 59% were classified as having \"good\" quality and 41% as \"acceptable\".