  In the context of air quality control, our objective is to quantify the
impact of uncertain inputs such as meteorological conditions and traffic
parameters on pollutant dispersion maps. It is worth noting that the majority
of sensitivity analysis methods are designed to deal with scalar or vector
outputs and are ill suited to a map-valued output space. To address this, we
propose two classes of methods. The first technique focuses on pointwise
indices. Sobol indices are calculated for each position on the map to obtain
Sobol index maps. Additionally, aggregated Sobol indices are calculated.
Another approach treats the maps as sets and proposes a sensitivity analysis of
a set-valued output with three different types of sensitivity indices. The
first ones are inspired by Sobol indices but are adapted to sets based on the
theory of random sets. The second ones adapt universal indices defined for a
general metric output space. The last set indices use kernel-based sensitivity
indices adapted to sets. The proposed methodologies are implemented to carry
out an uncertainty analysis for time-averaged concentration maps of pollutants
in an urban environment in the Greater Paris area. This entails taking into
account uncertain meteorological aspects, such as incoming wind speed and
direction, and uncertain traffic factors, such as injected traffic volume,
percentage of diesel vehicles, and speed limits on the road network.
