A statistical emulator for multivariate model outputs with missing values

Statistical emulators are used to approximate the output of complex physical models when their computational burden limits any sensitivity and uncertainty analysis of model output to variation in the model inputs. In this paper, we introduce a flexible emulator which is able to handle multivariate model outputs and missing values. The emulator is based on a spatial model and the D-STEM software, which is extended to include emulator fitting using the EM algorithm. The missing values handling capabilities of the emulator are exploited to keep the number of model output realisations as low as possible when the computing burden of each realisation is high. As a case study, we emulate the output of the Atmospheric Dispersion Modelling System (ADMS) used by the Scottish Environment Protection Agency (SEPA) to model the air quality of the city of Aberdeen (UK). With the emulator, we study the city air quality under a discrete set of realisations and identify conditions under which, with a given probability, the 40 μgm−3 yearly average concentration limit for NO2 of EU legislation is not exceeded at the locations of the city monitoring stations. The effect of missing values on the emulator estimation and probability of exceedances are studied by means of simulations.