## 2 Comparative Method
### Scaling Approach
#### 2.3.1 Comparing Climate Mitigation Potentials for Different In-Flight OIs  
Each in-flight OI's climate mitigation potential is assessed for a _reference flight plan_ defined by the study scope, e.g., representative missions or a specific airline network. Our goal is to extend these estimates to a _target flight plan_ which corresponds to the overall missions of interest for the comparison. The applied scaling approach of climate effects is schematically described in Figure 2.  
Figure 1: Applied proxies for scaling of mitigation potentials (dashed line: traffic size proxy, dotted line: required scaling parameter for in-flight non-CO\({}_{2}\) effects). First, the traffic-size-related scaling is performed to consider effects from different flight frequencies, aircraft types and the associated fuel consumption as well as CO\({}_{2}\) effects. This effect is modeled with the ASK-related scaling factor \(a\) calculated as  
\[a=\frac{ASK_{target}}{ASK_{reference}} \tag{1}\]  
where \(ASK_{target}\) defines the sum of ASK for the target flight plan for which the climate impact is to be estimated based on the reference flight plan with \(ASK_{reference}\). Second, CO\({}_{2}\)-Eq-related scaling is performed to incorporate the mission-specific dependency between CO\({}_{2}\) and non-CO\({}_{2}\) effects, which are defined by:  
\[CO_{2}Eq=\frac{ATR100_{total}}{ATR100_{CO_{2}}} \tag{2}\]  
To avoid computationally extensive calculations, a simple approach to estimate route-specific CO\({}_{2}\)-Eq can be applied as presented by [PERSON] et al. [66]. The authors introduce a regression model to calculate CO\({}_{2}\)-Eq for non-CO\({}_{2}\) emission in dependence of flight distance and average latitude from origin and destination airports per mission as follows:  
\[CO_{2}Eq=1+f_{NO_{2}}(\[PERSON]_{orig},\[PERSON]_{dest},D)+f_{H_{2}O}(\[PERSON]_{orig},\[PERSON]_ {dest},D)+f_{CIC}(\[PERSON]_{orig},\[PERSON]_{dest},D) \tag{3}\]  
with \(CO_{2}Eq\) as the climate impact in CO\({}_{2}\) equivalents of ATR100 for a specific route with a distance of \(D\) and latitude of origin and destination airport described by \(\[PERSON]_{orig}\) and \(\[PERSON]_{dest}\), respectively. A detailed description of the functions per climate species (\(f_{NO_{2}}\), \(f_{H_{2}O}\), and \(f_{CIC}\)) can be found in [PERSON] et al. [66]. Alternatively, the CO\({}_{2}\)-Eq of a reference or target flight plan can also directly be derived from detailed calculations, if the reference case results are available for the target flight plan. It needs to be considered that the method to estimate route-specific CO\({}_{2}\)-Eq also determines if seasonal differences can be considered or annually aggregated mean values are included. Subsequent to the CO\({}_{2}\)-Eq calculation, the respective scaling factor \(c\) can be determined as follows:  
\[c=\frac{CO_{2}Eq_{target}}{CO_{2}Eq_{reference}} \tag{4}\]  
where \(CO_{2}Eq_{target}\) defines the average CO\({}_{2}\)-Eq for target flight plan for which the climate impact is to be estimated based on the reference flight plan with a CO\({}_{2}\)-Eq of \(CO_{2}Eq_{reference}\). Finally, both scaling aspects can be combined to estimate \(ATR_{target}\) for the target flight plan by applying the previously calculated scaling factors:  
\[ATR_{target}=a\cdot c\cdot ATR_{reference} \tag{5}\]  
The scaling approach of climate effects can further be improved with flight matching in a pre-processing step. The goal of the matching approach is to find the best suitable  
Figure 2: Schematic illustration of scaling approach for in-flight OIs incorporating differences in traffic size and non-CO\({}_{2}\) effects between reference and target flight plan. reference flight for every selected target flight used for scaling. Selection criteria can be determined by differences in flight distance, origin, and destination airport location, or aircraft type. Validation of the introduced scaling approach is performed based on the individual assessment of the results from the ISOC study, presented in Appendix B.