With increased pollutant emissions and exposure due to mass urbanization worldwide, air quality measurement campaigns and epidemiology studies on air pollution and health effects have become increasingly common to estimate individual exposures and evaluate their association to various illnesses. Air quality simulations at urban scale are a key tool for the evaluation of population exposure to particulate matter and gaseous air pollutants. While modeling methods of various sophistication exist, these models depend on varying parameters such as traffic demand and emissions, and meteorological conditions, often unknown at the micro scale. In addition, atmospheric dispersion models generally make assumptions of simplified or unknown physics, and have high computational costs. The simulations are thus expensive and subject to high uncertainties that originate from various sources, especially from unknown or sparsely represented input data. The quantification of the resulting uncertainties is an important topic, particularly in the context of the assimilation of observational data. This task is no simple feat, considering the computational expense of detailed, small-scale numerical models. The objective of our work is to study the uncertainties in a simulation chain, which includes a dynamic traffic assignment model, an emission model and an atmospheric dispersion model at urban scale, using meta-modeling by projection-based dimensional reduction throughout the chain to reduce computational costs.
The domain of study in this work is the metropolitan area of Clermont-Ferrand (France). In this rich case study, we have access to two years of hourly observation data on traffic flow and pollutant concentrations. We have a representation of the road network and urban geometry, data on traffic demand, vehicle fleet, meteorological observations, background pollutant concentrations and background surface emissions, provided by the city of Clermont-Ferrand and the French company NUMTECH, a leader in environmental modeling and data science. An agreement with NUMTECH has been signed to continue this important collaboration.
We began with the meta-modeling of the computationally intensive simulation chain, using reduced basis of the model output spaces, and surrogate approximations of the projection of a state onto the basis. The traffic assignment model has been meta-modeled in , and after dimensional reduction of the input space by a reduced basis representing pollutant emissions, the atmospheric dispersion model is replaced by a meta-model for concentration of NO2 at street scale . This meta-modeling technique has the advantage of relying on a reduced basis which represents the predominant behaviors of the model solutions, but with a non-intrusive method of approximating projection coefficients and implementation at much lower computational cost than the full model.
Uncertainty in inputs can be represented by probability density functions (PDFs) on each varying model parameter, throughout the simulation chain, such as traffic demand for the traffic model, composition of the vehicle fleet for emission estimation, and meteorology for the atmospheric dispersion, as well as uncertainty propagated from the traffic and emissions models to the inputs of the dispersion model. We also consider the uncertainty propagation due to the dimensional reduction necessary for computational costs of numerous model runs. We study the propagation of uncertainty in the complete chain, using Markov chain Monte Carlo (MCMC) simulation and probabilistic scores. The simulations are compared to observations, mainly pollutant concentrations at air quality monitoring stations, and traffic observations at loop counters used in the computation of traffic demand inputs. The goal of this uncertainty quantification is to find a representation of the distributions of the model input parameters, which are considered to be of stochastic nature with deterministic approximations in practice, based on this comparison to observation data. MCMC methods are computationally very expensive, precluding application to large-scale operational models for urban air quality. Our meta-model chain, in combination with extensive observation data, allows us to study these otherwise inaccessible methods. We want to take full advantage of the wealth of data available in this case study by using many observations to determine parameter distributions, which nevertheless requires significant computational resources despite the great reduction in approximation time by the meta-models.
 Chen, Ruiwei, et al. Metamodeling of a Dynamic Traﬃc Assignment Model at Metropolitan Scale.
 Hammond, J. K., et al. “Meta-Modeling of a Simulation Chain for Urban Air Quality.” Advanced Modeling and Simulation in Engineering Sciences, vol. 7, no. 1, Sept. 2020, p. 37. BioMed Central, doi:10.1186/s40323-020-00173-2.