The EMEP4UK model is a regional application of the EMEP MSC-W (European Monitoring and Evaluation Programme Meteorological Synthesizing Centre-West) open-source ACTM (https://www.github.com/metno/emep-ctm, version rv4.8, last access: 11 June 2018). The detailed description of EMEP MSC-W is available from Simpson et al. (2012), and the EMEP4UK model is described by Vieno et al. (2010, 2014, 2016a).

EMEP4UK is a 3-D one-way nested Eulerian model with a horizontal resolution of 5 km × 5 km over the British Isles nested within an extended European domain with 50 km × 50 km resolution. The extent of the inner domain is shown in Fig. 1. The model has 20 vertical levels, extending from the ground to 100 hPa with the lowest vertical layer at ∼90 m. The model time step is 20 s for chemistry, 5 min for the advection in the inner domain, and 20 min for the advection in the outer domain.

The meteorological fields were computed using Weather Research and Forecast model version 3.1.1 (http://www.wrf-model.org/, last access: 15 November 2017) (Skamarock et al., 2008). The WRF model initial and boundary conditions are derived from the US National Center for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) Global Forecast System (GFS) at 1∘ resolution, including Newtonian nudging every 6 h (NCEP, 2000).

The anthropogenic emissions of sulfur dioxide (SO2), nitrogen oxides (NOx), ammonia (NH3), fine and coarse primary particulate matter (PM2.5, PMcoarse), carbon monoxide (CO), and non-methane volatile organic compounds (NMVOC) for the UK were derived from the National Atmospheric Emissions Inventory (http://naei.beis.gov.uk/, last access: 15 October 2015). For the outer domain, the emissions are provided by the Centre for Emission Inventories and Projections (CEIP; http://www.ceip.at/, last access: 15 October 2017). All emissions are split across a set of emission source sectors defined by the Selected Nomenclature for Air Pollutants (SNAP) described in Table 1. The hour-of-day, day-of-week, and monthly emission factors are used to distribute the annual total emissions temporally to hourly resolution as described in Simpson et al. (2012). The international shipping emissions were derived from ENTEC UK Ltd. (now Amec Foster Wheeler) (Entec, 2010). Biogenic emissions of dimethyl sulfide in addition to monthly in-flight aircraft, soil, and lightning NOx emissions are included as described in Simpson et al. (2012). Biogenic emissions of monoterpenes and isoprene are calculated by the model for every grid cell and time step according to the methodology of Guenther et al. (1993, 1995) using near-surface air temperature and photosynthetically active radiation as well as aggregated land-cover categorisations, as described in Simpson et al. (2012). The emissions of sea salt and wind-blown dust are also included. The details of the sea salt generation parameterisation scheme used in the model are presented in Monahan et al. (1986) and Mårtensson et al. (2003). The boundary condition monthly average concentrations of fine and coarse dust are calculated with the global chemical transport model of the University of Oslo (Grini et al., 2005); the detailed parameterisation of dust mobilisation is presented in Simpson et al. (2012).

The chemistry, aerosol formation, and wet and dry deposition schemes are as described in Simpson et al. (2012). The chemistry scheme has 72 species and 137 reactions, and the gas–aerosol partitioning is described by the MARS formulation. A detailed evaluation of model performance is discussed elsewhere (Vieno et al., 2010, 2016b; Dore et al., 2015; Lin et al., 2017). In our study, all model runs were executed using meteorology and emissions data for the year 2012.

In this study, emissions of all of the major primary anthropogenic pollutant compounds were investigated. The decision to concentrate on anthropogenic emissions was made based on the fact that one of the main applications of the EMEP4UK model is providing scientific support for policy-making regarding the impacts of interventions leading to anthropogenic emissions reductions. Hence, the potential future changes in emissions driven by environmental and climate change policies are not likely to affect biogenic emissions as much as anthropogenic emissions. Therefore, it was decided to investigate model response to the changes in anthropogenic emissions.

For this study, emissions of five pollutants (NOx, SOx, VOC, NH3, primary PM2.5) were split into 13 model input variables based on the contributions from different emission source sectors to total annual emissions; the emissions from the dominant sector (the sector with the highest relative contribution to total emissions) for every pollutant were treated as a separate variable, while the emissions from the rest of the sectors were grouped and treated as another input variable. Shipping emissions were treated as a separate variable and were not split by the pollutant type. The description of the SNAP sectors is shown in Table 1, and the definitions of the input variables for the uncertainty and sensitivity analyses in this work are presented in Table 2, where variables marked with D represent emissions from a single dominant sector (D1 and D2 in the case of multiple dominant sectors) and variables marked with O indicate the grouped “other” emissions from the rest of the sectors. Emissions from “natural” sources (e.g. lightning, soil, ocean) were not part of the uncertainty and sensitivity analyses.

Uncertainty ranges for the input emissions from UK anthropogenic land-based sources were assigned according to data in the UK Informative Inventory Report (IIR) (Wakeling et al., 2017). In the IIR, uncertainties are defined as upper and lower limits of the 95 % confidence interval relative to the central estimate. There is no information on uncertainty ranges for different source sectors available for the emissions for 2012 because uncertainties split by the emission source sector were first presented in the IIR that included 2014 emissions (Wakeling et al., 2016). Hence, for this study, the most recently published data for the uncertainty ranges of pollutants split by source sector were used.

Equation (1) was used to aggregate uncertainties for multiple emission source sectors for the grouped-source input variables, where x is the quantity of interest and U is the uncertainty of that quantity, taken from the EMEP/EEA air pollutant emission inventory guidebook (Pulles and Kuenen, 2016).

Utotal=(U1x1)2+(U2x2)2+⋯+(Unxn)2x1+x2+⋯+xn

The shipping emission variable in this study combines all emissions of all relevant pollutants, and hence a “best estimate” range for the uncertainty was chosen. The range was estimated based on the available published information. The shipping emissions were not split by pollutant because the inclusion of the split for this source comprised too great a computational cost for the analyses. Most shipping emissions do not impact land-based population and ecosystem exposure, which was our focus, compared with terrestrial emissions.

Some recently published sources (Corbett, 2003; Scarbrough et al., 2017) state that the uncertainty in shipping emissions is significant, but do not provide quantitative estimates. The most recent source of quantitative information on the uncertainty in shipping emissions is the report for the European Commission (Entec, 2002) which presents the estimates of uncertainties for emission factors of NOx, SO2, PM, and VOC for shipping emissions “at sea”, “manoeuvring”, and “in port”. The uncertainties are presented for emissions in the year 2000 as 95 % confidence intervals (CIs) with the lowest values of uncertainty presented for “at sea” emission factors (±10 %–20 %) and the highest values for “manoeuvring” emission factors (±30 %–50 %). For the total pollutant emissions for the year 2000 the percentage uncertainties around the estimates are ±21 % for NOx, ±11 % for SO2, ±11 % for CO2, ±28 % for VOC, and ±45 % for PM. Additionally, in Moreno-Gutiérrez et al. (2015) the uncertainty in the emission factors for all pollutant compounds was estimated to be ±20 %. Using the above data, an overall uncertainty of ±30 % was assigned to the shipping emissions variable in this study (Table 2). It was applied to all shipping emissions within the inner British Isles domain of the EMEP4UK model.

A Gaussian process emulator was used to estimate model predictions at unsampled points in the space of the uncertain model inputs. The UQLab, a MATLAB-based software framework for uncertainty quantification (Marelli and Sudret, 2014; Lataniotis et al., 2017), was implemented to build the emulators for the uncertainty propagation and the following sensitivity analysis. A comprehensive description of the statistical theory of Gaussian process applied to uncertainty and sensitivity analysis with full mathematical details can be found in O'Hagan (2006) and Oakley and O'Hagan (2002, 2004).

The uncertainty values and sensitivity indices were calculated for three EMEP4UK model outputs (O3, NO2, and PM2.5 surface concentrations) with annual and monthly temporal resolution. For the annually averaged outputs, an emulator was created for each modelled grid cell in the EMEP4UK domain (n= 59 400). The first- and total-order sensitivity indices were calculated for the land-based grid cells only (n > 10 000). For the monthly mean model outputs, uncertainty and sensitivity analyses were performed for five selected grid cells. The five grid cells were selected to contain a UK national-network air pollution monitoring station to aid classification according to the environment (i.e. rural background, urban background, and urban traffic) and also to provide geographically representative coverage across the UK.

LHS maximin design, which maximises the minimum distance between the points in the parameter space to provide the optimum space-filling properties, was used. The design was previously demonstrated as suitable for Gaussian process emulators by Jones and Johnson (2009). A design with 84 data points was created for the scaling coefficients that were subsequently applied to the input emissions. This means that emissions corresponding to a particular input variable were perturbed homogeneously throughout the whole of the UK model domain. The ranges of scaling coefficient used for the sampling design are presented in Table 2. In this study, 84 sampling points were found to be sufficient to create an adequately performing emulator, as the input–output response function for the EMEP4UK model was expected to be smooth on monthly and annually averaged timescales. More generally, however, for the case in which model runs are computationally expensive and the input–output relationship is less predictable a sequential sampling technique can be applied to track the improvement of emulator performance with an increase in the sample size.

In this study, the surface concentration of O3, NO2, and PM2.5 for every grid cell is defined as a scalar output Y=f(X), where X is the vector of input values {X1, … , X13}.

A Gaussian process emulator utilises a Bayesian approach; training data are used to update the selected prior to produce posterior mean and covariance functions. The Gaussian process is specified by its mean function and covariance function. The mean function is given by Eq. (2): E[f(x)|β]=h(x)Tβ, where h(⋅) is a vector of regression functions and β is a vector of unknown coefficients. The choice of h(⋅) incorporates any prior beliefs about the form of f(⋅). In this study, the mean function was chosen to have a linear form βo+∑i=113βixi on the basis that the response of the surface concentration to changes in input emissions is expected to be smooth with no discontinuities or fluctuations.

The covariance function between f(x) and f(x′) is given by Eq. (3): covfx,fx′|σ2=σ2c(x,x′), where σ2 is the hyperparameter that represents the variance of the Gaussian process and c(x,x′) is the correlation function. The correlation function increases as the distance between x and x′ decreases and equals 1 when x=x′. In this study Matérn 5/2 (Eq. 4) was used, where h is the absolute distance between x and x′, and θ is a vector of range parameters or length scales, which define how far one needs to move along a particular axis in the input space for the function values to become uncorrelated. cx,x′=1+5hθ+5h23θ2exp⁡-5hθ

A number of emulators were built with the EMEP4UK simulation data using other available covariance functions; however, little difference was found in the performance of the emulators. The hyperparameters β, σ2, and θ were estimated using a cross-validation approach.

The emulator error was estimated by implementing k-fold cross-validation (Urban and Fricker, 2010; Gladish et al., 2017). The original sample was randomly partitioned into k=10 subsamples, which allowed approximately 90 % of the data to be used as a training set and 10 % as a validation set. The spatial distribution of cross-validation errors is presented in the Supplement (Fig. S1).

Figure 2 shows the spatial distribution of annual average surface concentrations of O3, NO2, and PM2.5 modelled with EMEP4UK and their absolute and relative uncertainties given the uncertainties in UK pollutant emissions for each source sector shown in Table 2. The uncertainties are presented as a range ± the baseline value and represent the 95 % confidence interval. The maps represent the uncertainty in surface concentrations propagated from the uncertainties reported in the UK emissions (Wakeling et al., 2017) and estimated uncertainties in shipping emissions in the EMEP4UK model domain (Entec, 2002; Moreno-Gutiérrez et al., 2015). The uncertainties in surface concentration do not incorporate any uncertainties in the spatial and temporal aspects of the input emissions because no data on these aspects of uncertainty are provided by the compilers of the emissions inventories.

For O3 and NO2 the areas with the highest uncertainty coincide with the locations of shipping lanes. This is due to assigning all shipping emissions an uncertainty of ±30 %, which causes high variability in the corresponding NOx emissions. The uncertainty in O3 surface concentrations for the land-based grid cells is generally low (median relative uncertainty is ±0.6 %) with values of uncertainty up to ±7 % or ±1.4 ppb occurring in the grid cells containing major UK cities. The overall low uncertainty in the modelled O3 concentrations can be attributed to the combination of a low uncertainty in precursor emissions and the substantial contribution of hemispheric background O3 to UK ambient concentrations, which are not part of this analysis of uncertainty with respect to the UK-only emissions (Simpson et al., 2012).

The relative uncertainty of NO2 has a homogeneous spatial pattern (median relative uncertainty for all land-based grid cells is ±7.4 %), while absolute uncertainty is found to be higher (up to ±3.5 µg m-3 or ±9 %) in areas with major UK cities. The magnitude of uncertainty in NO2 is determined by the combination of two factors: (i) NO2 uncertainty is driven by NOx emission inputs, which have low levels of uncertainty associated with them, and (ii) low overall variation in O3 surface concentrations affects the reactions between NO, NO2, and O3 that are linked through the photolysis of NO2 to give NO and the reaction of NO with O3 to produce NO2.

The spatial pattern of PM2.5 surface concentrations and the corresponding absolute and relative uncertainties differ from those for O3 and NO2. The concentration gradient indicates the presence of transboundary PM2.5 transport into the UK. This is consistent with findings reported by AQEG (2013) that only about half of the PM2.5 annual average concentrations have a UK origin. The spatial pattern of uncertainty in PM2.5 concentrations shows higher uncertainty, both relative and absolute, in the grid cells with major cities; median relative uncertainty for all land-based grid cells is ±4.6 % with up to ±9 % (±0.9 µg m-3) in the grid cells with major cities. The surface concentrations of PM2.5 are dominantly comprised of primary PM2.5 emissions and inorganic aerosols resulting from chemical reactions between SO2, NOx, and NH3. Hence, the spatial pattern of uncertainty can be explained by the fact that the main contribution to primary PM2.5 comes from emissions from sources such as stationary combustion (e.g. residential heating) and road transport. The pattern of decreasing uncertainty from the land-based grid cells (centre) towards the edges of the domain indicates a change in variation due to the transport of PM2.5 away from the sources of emitted pollutants.

The overall uncertainty in the output variables (O3, NO2, and PM2.5) was found to be lower compared to the uncertainty of the model input emissions. This can be explained by the overall weak response of surface concentrations to changes in emissions originating from the UK, which leads to the conclusion that surface concentrations are affected by the transport of pollutants from elsewhere. Another explanation is the so-called “compensation of errors” whereby a positive effect of one or multiple input variables on the output is compensated for by a negative effect of other input variables. This leads to the narrower confidence intervals associated with EMEP4UK outputs (Skeffington et al., 2007).

An important observation from this uncertainty analysis is that the areas with the highest uncertainty coincide with the most populated areas. Given that O3, NO2, and PM2.5 are associated with adverse health effects, it is particularly important to have an estimate for the confidence level of the modelled values in more densely populated regions. This work has shown that the highest uncertainty is precisely in these regions. The reason for the increased levels of uncertainty in the grid cells coinciding with urban areas is discussed below.

In addition to quantitative uncertainty estimates, it is of interest to know how the uncertainty of each input contributes to the overall uncertainty and whether there are interactions between inputs that potentially affect the magnitude of overall uncertainty. This was achieved by conducting a variance-based sensitivity analysis.

Figures 3, 4, and 5 show the spatial distribution of the first-order sensitivity indices that represent the fractional contribution of the uncertainty of each input variable to the overall uncertainty in the output. Only the variables with Si>0.03 are presented here. First-order indices with values less than 0.03 were omitted as the method used for computation of sensitivity indices is prone to numerical errors when the analytical sensitivity index values are close to zero (Saltelli et al., 2006). The threshold was estimated by examining the noise in first-order sensitivity indices calculated for unimportant input variables. Excluding Si<0.03 does not have an effect on the results presented because a relative contribution of less than 3 % to the overall uncertainty can be considered negligible.

The difference between total- and first-order sensitivity is used to highlight interactions between the variable Xi and all other input variables. For the sensitivity coefficients computed for the annual-averaged model outputs, there was no substantial difference found between first- and total-order sensitivity indices, and hence no between-input interactions were identified on the annual timescale (Fig. S2).

Figure 3 shows the spatial distribution of first-order sensitivity indices for the input variables affecting modelled O3 concentrations. It is predominantly the NOx input emissions that drive the uncertainty in modelled O3 surface concentrations.

The greatest contribution to O3 surface concentration uncertainty in areas with higher levels of overall uncertainty is from the input variable NOx_O, which represents NOx emissions from all the other SNAP sectors apart from SNAP 1 (combustion in the energy and transformation industries) and SNAP 7 (road transport). The NOx emissions combined into this input variable account for 27 % of total NOx emissions, and the uncertainty range for this variable is ±19 %. The input variable NOx_D1 (emissions from combustion in the energy and transformation industries) does not contribute substantially to output uncertainty despite making up 41 % of total NOx emissions, with a relative uncertainty of ±7 %. This is explained by the height at which these emissions occur; the emissions are injected into the vertical layers at heights of > 184 m above ground level. This leads to NOx being dispersed and transported away from these elevated sources without affecting ground-level O3 concentrations locally. The NOx emissions from the input variable NOx_D2 (road transport) account for the remaining 32 % of total NOx emissions. The spatial distribution of corresponding sensitivity indices indicates that uncertainty in road transport emissions affects overall uncertainty in O3 surface concentrations in the grid cells closest to the emission sources (i.e. major roads). A large proportion (> 80 %) of overall uncertainty in O3 concentrations in areas adjacent to the south and south-east coasts of England is apportioned to the uncertainty in shipping emissions.

In Scotland, most of the overall uncertainty in the O3 surface concentration is apportioned to the variables VOC_D and VOC_O that respectively represent VOC input emissions from the dominant VOC source sector (solvent and other product use) and emissions from the rest of the source sectors grouped into a single input. A small proportion is apportioned to the variable NH3_D that represents NH3 emissions from agricultural sources. The effect of these input variables manifests in Scotland because of low levels of locally emitted NOx. The overall uncertainty in this area is very low.

In summary, the uncertainty in modelled surface concentrations of O3 in densely populated areas can be apportioned to the uncertainty in NOx emissions from non-dominant sources and uncertainty in shipping emissions.

The uncertainty in the surface concentration of NO2 was found to be driven mostly by uncertainty in NOx emissions (variables NOx_D1, NOx_D2, NOx_O) and shipping emissions (Fig. 4). Similarly to O3, NO2 is most sensitive to NOx emissions combined from all SNAP sectors apart from SNAP 1 (combustion in energy and transformation industries) and SNAP 7 (road transport). There is almost no sensitivity to NOx emissions from SNAP 1 for the same reason given above that these are elevated emissions. The sensitivity to NOx emissions from SNAP 7 is most pronounced close to the source of emissions (i.e. major roads and cities).

The similarity in the spatial distribution of sensitivity indices for O3 and NO2 model outputs results from the concentrations of these pollutants being inversely correlated, as their chemical transformation reactions are interlinked. In the same way as for O3, uncertainty in the NO2 concentrations along the south and south-east coasts of England is mostly driven by uncertainty in shipping emissions. In fact, uncertainty in shipping emissions contributes approximately 30 % of uncertainty in NO2 concentrations, even well inland in areas away from major roads and cities.

Figure 5 shows the spatial distribution of first-order sensitivity indexes for the model inputs that contribute to the uncertainty in modelled surface concentrations of PM2.5. Modelled PM2.5 is sensitive to all emissions of NH3 (the dominant sector is agriculture), to primary PM2.5 (the dominant sector D1 is residential combustion and D2 is road transport), and to shipping emissions. In areas with lower surface PM2.5 concentrations such as Scotland, Wales, northern England, and south-west England, the uncertainty is mainly driven by NH3 emissions from agriculture (NH3_D). The spatial pattern of emission sensitivity indices for PM2.5 mirrors the spatial distribution of PM2.5 emission sources. From Figs. 2 and 5 it can be seen that in areas with the highest levels of uncertainty the model output is most sensitive to the emissions of primary PM2.5. Similar to the results for O3 and NO2, the areas with the highest uncertainty coincide with the most populated areas.

The pattern in calculated sensitivity indices partially agrees with a previous study of changes in PM2.5 surface concentrations in response to a 30 % reduction in emissions of PM2.5, NH3, SOx, NOx, and VOC by Vieno et al. (2016). In the study by Vieno et al. (2016) surface concentrations of PM2.5 were found to be sensitive to reductions in each of the five pollutants individually (the same reduction was applied to a pollutant's emissions from all SNAP sectors simultaneously), with the highest sensitivity to NH3 and PM2.5 emissions (up to an approximately 6 % reduction in surface concentration in response to 30 % reduction in emissions). In comparison, in our study the uncertainty in PM2.5 surface concentrations is not affected by the perturbations of SOx, NOx, and VOC. This is likely due to (i) the difference in ranges of variation (i.e. uncertainty ranges) in this study (SOx, NOx, and VOC input variables have narrower ranges of variation compared to PM2.5 and NH3) and (ii) the presence of non-additivity and non-linearity in the model response to perturbations in the inputs.

Uncertainty assessment and sensitivity analyses for monthly averaged surface concentrations of NO2, O3, and PM2.5 were performed for five different grid cells that were assigned the following environment types based on the site type attributed to the national-network monitoring site within that grid cell: Auchencorth Moss and Harwell – rural background; Birmingham Acocks Green and London N. Kensington – urban background; and London Marylebone Road – urban traffic.

Monthly average concentrations with error bars representing the absolute uncertainty values (as a 95 % CI) are presented in Fig. 6. Figure 7 shows corresponding values of the relative uncertainty. Figure 8 shows how the magnitude of first-order sensitivity indices estimated for five different grid cells changes on a monthly timescale. If all first-order sensitivity coefficients add up to 1 then there are no interactions between inputs and all model variance can be apportioned to the variance in the individual inputs.

The NO2 surface concentrations show a seasonal trend of lower concentrations occurring during summer months with the exception of the Auchencorth Moss grid cell in which NO2 concentrations are low throughout the year. The magnitude of uncertainty in NO2 is proportional to the modelled concentration and changes relative to the concentration, which can be seen from the monthly relative uncertainty values (Fig. 7). The first-order sensitivity indices for NO2 show that only NOx emissions (across all sectors) and shipping emissions influence the modelled surface NO2 concentrations. Hence, it can be concluded that the uncertainty in modelled concentrations of NO2 directly depends on the uncertainty in NOx emissions and is not affected by the uncertainties in the emissions of any other pollutant. The change in the magnitude of sensitivity coefficients for the Harwell grid cell indicates increasing influence of shipping emissions on NO2 concentrations during the summer months. A potential explanation for this is a seasonal change in the wind direction, which results in more NOx from shipping emissions being transported to the grid cell during the summer months (the wind rose is presented in Fig. S3).

The uncertainties in the O3 modelled surface concentrations show an inverse seasonal trend compared to the uncertainties in modelled NO2. Unlike the uncertainty in the NO2 concentration, the uncertainty in the O3 concentration is influenced by the grid cell environment type; the highest level of uncertainty is observed for the London Marylebone Road grid cell (urban traffic). The relative uncertainty in O3 concentrations for the Auchencorth Moss grid cell (rural background) is small and close to the median relative uncertainty in O3 for annual average concentrations, which as discussed above is ±0.6 %. This indicates that perturbations in the input emissions do not substantially affect the O3 concentration in this grid cell. Although the magnitude of uncertainty in O3 is very small in this grid cell, the inputs that drive it differ noticeably throughout the year; during May–August the variance is mostly explained by VOC emissions (explains 77 % of uncertainty for July) and during November–February NOx emissions drive the uncertainty. The magnitude of O3 concentrations and corresponding uncertainties in the Birmingham Acocks Green and Harwell grid cells is very similar. The trends in sensitivity indices are also similar; during the April–September period some variance in the model output is explained by uncertainty in VOC emissions. However, in the Harwell grid cell shipping emissions play a more important role. For the London-based grid cells, the level of uncertainty is the highest and is mainly driven by the uncertainty in NOx and shipping emissions.

For the PM2.5 monthly average concentrations, London-based grid cells show the highest values of absolute uncertainty and Auchencorth Moss the lowest. The relative uncertainty in London-based grid cells is also the highest. From Fig. 7 it can be seen that the contribution to the overall uncertainty from the uncertainty due to NH3 emissions for these grid cells is not as important as for other three; the majority of uncertainty is explained by the uncertainty in the primary PM2.5 emissions with PM2.5 from road transport being the dominating variable. In Birmingham Acocks Green and Harwell, the effect of NH3 emissions from agricultural sources is more pronounced; from 30 % to 70 % of overall uncertainty in PM2.5 can be apportioned to uncertainty coming from agricultural emissions of NH3 during spring and summer months.

There are published studies that apply global sampling-based uncertainty and sensitivity analyses as well as derivative-based methods (methods that do not have limitations of local OAT, i.e. linearity assumption) to ACTMs. However, the results reported by these studies are mostly of use for model development and calibration purposes and not the assessment of confidence in the model predictions and outputs. This is mainly because the simulations are performed for a short period ranging from days (Rodriguez et al., 2007; Chen and Brune, 2012; Beddows et al., 2017) to weeks (Cohan et al., 2010; Shrivastava et al., 2016).

Additionally, in some studies, commercial software or packages with a graphical user interface (GUI) are used for global sensitivity and uncertainty analysis (Lee et al., 2011; Chen and Brune, 2012; Christian et al., 2017). These tools are well designed for a specific purpose but lack the option to scale up and to automate the analysis, i.e. the ability to calculate sensitivity indices and uncertainty ranges for thousands of grid squares automatically.

Our study addresses both of the shortcomings. We demonstrate sensitivity and uncertainty analyses for the ACTM for a whole year for the UK domain as well as investigate variations in sensitivity and uncertainty on the monthly timescale for multiple locations with different environmental characteristics. Additionally, the package used to create Gaussian process emulators and to conduct uncertainty and sensitivity calculations is fully customisable and can be adapted for any application.

The model runs generated for the global sensitivity and uncertainty analysis can be utilised for other purposes provided that the sampling range for all inputs of interest is wide enough. For example, in our study the training points for the Gaussian emulator were selected to cover a wider range of input perturbations compared to the corresponding uncertainty range (Table 2). For all input emissions of SOx, NOx, VOC, and NH3 the ranges of variation for the LHS design were set to ±40 % of their baseline value; for primary PM2.5 emissions the range was set to ±75 % and for shipping emissions from -40 % to +100 %. Hence, the emulators created in this study using the model runs within the aforementioned input space can be used to investigate other scenarios of the model response to input emission perturbations with no extra computational cost. Hence, alternative ranges and probability distributions can be assigned to the model inputs to estimate the resulting output uncertainty or the emulator can be used for various emission reduction scenario analyses.

Finally, in this study the overall model output uncertainty is likely to be lower than the theoretical total model output uncertainty, as in addition to the input emissions there are a variety of other uncertain model inputs. Assessing the effect of variation in every model input and parameter on the model output is a laborious task; hence, ideally sensitivity analysis should be incorporated as a part of the model development process. By using this approach, the effect of all uncertain inputs and parameters could be assessed without having to do it retrospectively.