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In the context of air quality control, our objective is to quantify theimpact of uncertain inputs such as meteorological conditions and trafficparameters on pollutant dispersion maps. It is worth noting that the majorityof sensitivity analysis methods are designed to deal with scalar or vectoroutputs and are ill suited to a map-valued output space. To address this, wepropose two classes of methods. The first technique focuses on pointwiseindices. Sobol indices are calculated for each position on the map to obtainSobol index maps. Additionally, aggregated Sobol indices are calculated.Another approach treats the maps as sets and proposes a sensitivity analysis ofa set-valued output with three different types of sensitivity indices. Thefirst ones are inspired by Sobol indices but are adapted to sets based on thetheory of random sets. The second ones adapt universal indices defined for ageneral metric output space. The last set indices use kernel-based sensitivityindices adapted to sets. The proposed methodologies are implemented to carryout an uncertainty analysis for time-averaged concentration maps of pollutantsin an urban environment in the Greater Paris area. This entails taking intoaccount uncertain meteorological aspects, such as incoming wind speed anddirection, and uncertain traffic factors, such as injected traffic volume,percentage of diesel vehicles, and speed limits on the road network.

Sensitivity analysis for sets : application to pollutant concentration maps