Abstract
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.
Highlights
Air pollution is one of the most important environmental problems because of its impact on people's health
It can be seen that, though the box-plot increases in height when moving from p = 1 to p = 4, most of the estimates x1,t are within the confidence interval of x10 and RF only reaches 3% when p = 4. This suggests that missing values do not compromise the emulator and, in turn, the estimate of the action to be taken to reduce the pollutant concentration at the desired level
This paper provides an empirical proof of the capabilities of a multivariate emulator, which is suitable for emulating physical model outputs where the output is vector-valued
Summary
Air pollution is one of the most important environmental problems because of its impact on people's health. Let y0 (x) = (y10 (x), ..., yM0 (x))′ be the yearly average pollutant concentration vector in any future year under a given realisation xi. SEPA uses the ADMS to predict pollutant concentrations at the city level, at hourly temporal resolution and at 75 m spatial resolution. This is done to understand under which conditions (of emissions, traffic, meteorology, etc.) the annual ambient pollutant concentration complies with the limits of the air quality directive (2008/50/EC). Since compliance with the directive is based on the concentrations measured at the monitoring stations, the ADMS output analysis is restricted to the spatial locations of the stations, installed in Aberdeen (Fig. 1). A main advantage of the emulator is that it directly provides an annual average for the pollutants, whereas when using the ADMS annual average of the pollutant has to be estimated from hourly simulations
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