**6. Conclusions**

Decision-making in multifaceted environmental arenas requires complex computational modelling and, thus, clever analytics and visualization solutions that are able to capture multiple dimensions, simultaneously. Monte Carlo simulation modelling has frequently been employed to integrate the uncertain inputs and to construct probability distributions of the resulting outputs. Visual analytics and data visualization can be used to support the processing, analyzing, and communicating of the influence of multi-variable uncertainties on the decision-making process. SimDec enables one to observe the output distribution of the variables of interest and simultaneously trace which components of the output distribution are attributable to specific combinations of the input variables.

In this study, SimDec was used to decompose a Monte Carlo model of the flying range of all-electric aircraft based upon improvements to batteries and electric motors. While the analysis focused upon the flying range for electrified aircraft, the distance findings extend directly into corresponding environmental and economic benefits. The decomposed results show that: (i) increased battery specific energy leads to increased flight distance; (ii) increased motor specific power has a significant effect when the batteries' specific energy is high; and, (iii) there is a decrease in the marginal benefits from motor improvement, alone. While the first observation cannot be considered surprising because there is a linear relationship between flight range and battery specific energy (Equation (5)), the latter two findings would not be inherently obvious to decision-makers without specialized aeronautical engineering backgrounds, and the SimDec analysis provides a perfect means to effectively demonstrate and communicate them.

The aviation electrification problem has illustrated how SimDec enables the simultaneous projection from combinations of multi-variable input uncertainties directly onto an output distribution. It demonstrated how SimDec stratified two sources of electrification uncertainty into distinct, coloured partitions that enabled a visualization of previously unidentified cause-and-effect influences of input variable combinations onto the flight distance output in the R&D investment analysis of aviation electrification. Since SimDec computations can be run concurrently with any Monte Carlo model with only negligible additional overhead, SimDec could easily be extended into the analysis of any environmental application that uses simulation—not just aircraft electrification. This generalizability, in conjunction with its straightforward visualizations of complex stochastic uncertainties, makes the practical contributions of SimDec very powerful in environmental decisionmaking. The efficacy for extending SimDec into more diverse environmental and sustainability applications beyond aviation electrification will be considered in future research.

**Author Contributions:** Conceptualization, M.K. and J.S.Y.; data curation, M.K. and T.N.; formal analysis, M.K.; methodology and validation, T.N.; writing—original draft preparation, M.K. and J.S.Y.; visualization, M.K.; writing—review and editing, J.S.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Natural Sciences and Engineering Research Council grant number OGP0155871, and by Finnish Foundation for Economic Foundation grant number 200153.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Acknowledgments:** The inspiration for this work was kindly provided by the eMAD team, including Juha Pyrhönen, Ilya Petrov, and Alexander Matrosov. The authors appreciate the fruitful and inspiring discussions with Nisse Nurmi on the state of the aviation industry.

**Conflicts of Interest:** The authors declare no conflict of interest.
