Attributing climate or air quality degradation to sources is challenging with sensitivity analysis techniques based on standard model output (Capps et al 2012). Yarwood et al (2007) broadly classifies two types of approach for determining source apportionment of particulate matter with techniques nested in the host models: Sensitivity analysis and reactive tracers. It is useful to distinguish between sensitivity analysis methods and uncertainty methods following Rao (2005), as the two terms are often used interchangeably. Sensitivity analysis is the systematic study of the behavior of a model over ranges in variation of inputs and parameters. Uncertainty analysis is the quantitative assessment of how the uncertainties in model physics and input data, as well as the random variability in input parameters, propagate through the model to give a single measure of uncertainty in the model results. Determining the importance of uncertainties in model components and model inputs to predictions of PM2.5 is very important when evaluating effectiveness of control strategies.
Historically, multiple air quality model simulations using different sets of emissions have been used to evaluate the expected benefit of different strategies. This approach is resource-intensive (Zhang et al 2013) leading to the development of new uncertainty analysis methods discussed briefly in this section.
The more complex the model, the more challanging the analysis becomes. For example, Fine et al (2003) note that many model sensitivity evaluations have been conducted using trajectory models because of their computational and input simplicity advantages, though recent efforts in the US have used Eulerian models. It is easier to work with trajectory models, but their simplifying assumptions are violated more readily (Fine et al 2003).
The simplest and most frequently used sensitivity analysis is the perturbative approach. Often referred to as the brute force method (BFM), a parameter value is perturbed, the model is rerun, and the change in observables is calculated to determine sensitivity coefficients (Fine at al 2003). The brute force method estimates first-order sensitivity coefficients (e.g., dSO4/dSOx) by making a small input change (dSOx) and measuring the
is inefficient because a complete model run is required for each sensitivity (Yarwood et al 2007). There have been few, if any, UK regional modelling studies that have not followed the ‘one parameter at a time’ (OAT) sensitivity analysis method. Rao (2005) notes that these sensitivity analyses will be fairly accurate in a weak response regime where the output is linearly related to the inputs for a base case with a specific value for each input variable (Rao 2005). The difficulty with OAT methods is inability to capture the true effect of non- linear dependencies among the input parameters. While Monte Carlo techniques propagate probability distributions through a large number of model simulations, the applicability of such techniques are largely limited to models with the lowest computational burden such as the Gaussian plume trajectory models which tend to lack the process level descriptions key to PM2.5 formation. Lee et al (2011) note that the Met Office Hadley Centre quantifying
uncertainty in model predictions (QUMP) project has resulted in several sensitivity studies undertaken using climate models attempting to improve on the OAT approach (Murphy et al., 2004)
Rao (2005) describes the use of uncertainty analysis in atmospheric dispersion modeling. They have also been applied to box-model simulations (e.g. Milford et al 1992; Derwent and Hov, 1988). As Yarwood et al (2007) state however, source apportionment for primary PM is relatively simple to obtain from any air pollution model because source-receptor relationships are essentially linear for primary pollutants. The Gaussian and Lagrangian approaches work for primary PM because the models can assume that emissions from separate sources do not interact. This assumption breaks down for secondary PM2.5 pollutants (e.g., sulfate,
nitrate, ammonium, secondary organic aerosol) and so puff models may dramatically simplify the chemistry (to eliminate interactions between sources) so that they can be applied to secondary PM. ApSimon and Oxley (2010) note that, for example, using the UKIAM lagrangian dispersion model care, has to be taken where there are non-linear chemical interactions between pollutants. For example, reducing ammonia emissions can have a large effect in reducing nitrate aerosol concentrations as well as ammonium ions, because of its role in the formation of ammonium nitrate. This is important because it magnifies the importance of ammonia in reducing secondary particulate concentrations (ApSimon and Oxley 2010).
Whilst Eulerian grid models are noted to be better suited to modeling secondary pollutants they do not naturally provide source apportionment because the impact of all sources has been combined in the total pollutant concentration (Yarwood et al 2007). This has lead to the development of numerical methods that are employed within the host model. On that basis there are a number of approaches in which sensitivity differential equations are derived from the original parent equations and solved at the same time (Zhang et al 2013). The equations can be derived analytically, as in the decoupled direct method (DDM). Most DDM applications focused on first-order sensitivity equations. A separate set of equations has to be derived for higher-order sensitivity coefficients. (Fine et al 2003). The DDM provides the same type of sensitivity information as the brute force method but using a computational method that is directly implemented in the host model (Dunker, 1981). This method operates integrally within a chemical transport model and simultaneously computes local sensitivities of pollutant concentrations to perturbations in input parameters. Zhang et al (2013) describe the development of the high-order decoupled direct method in three dimensions for particulate matter (HDDM-3D/PM) to enable advanced sensitivity analysis of ISORROPIA, the inorganic aerosol module of CMAQ (specifically the authors implement this in CMAQ v4.5). They state that although nonlinear effects of aerosol precursors on aerosol concentrations have been of concern in the past decade (Ansari and Pandis, 1998; West et al., 1999), developing HDDM for PM has not yet been undertaken due to the discontinuous, highly nonlinear solution surface of the inorganic aerosol thermodynamics. At the present time, there appears to be no extension to account for any SOA mechanism.
et al 2003). Capps et al (2012) state that adjoint-based sensitivity analysis enhances the ability to assess the relative influence of aerosol precursor emissions on air quality metrics as well as providing a means of refining emissions estimates with observations in an inverse modeling framework. Moreover, the authors state that the adjoint method complements forward sensitivity approaches by efficiently elucidating the relationship of model output (e.g., specified concentrations, air quality metrics) to the field of model parameters, or input, (e.g., emissions, initial conditions) without perturbing model inputs. Computational requirements for calculation of these receptor-oriented sensitivities are insensitive to the number of model parameters investigated. Of the modules incorporated in models used in the UK, again developments have been limited to the inorganic thermodynamic model ISORROPIA, as implemented in CMAQ and the PTM. The adjoint version, ANISORROPIA (the AdjoiNt of ISORROPIA, an aerosol thermodynamic model), was developed by Capps et al (2012) to determine the sensitivity of fine mode aerosol concentrations to inorganic aerosol precursor concentrations. In the adjoint of a chemical transport model, it can be used to assess the relative contributions of emissions from different sources at various times and places. At present, there is only evidence of incorporation of ANISORROPIA into the adjoint models of GEOS-CHEM (e.g. SIA sensitivity by Henze et al 2009) and CMAQ for non-UK use. There is however evidence of use for the adjoint in determining source contributions to ozone, an important oxidant and determinant of SOA. Zhang et al (2009) used the GEOS- Chem adjoint to quantify source contributions to ozone pollution at two adjacent sites on the U.S. west coast.