The nitrate-extended version of the GLOMAP-mode coupled model (GMV4-nitrate) is based on the GLOMAP-mode aerosol microphysics model described above and by Mann et al. (2010).
The nitrate-extended model includes an additional inorganic dissolution solver to accurately characterise the size-resolved partitioning of NH3 and HNO3 into NH4 and NO3 components in
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each soluble mode (Benduhn et al., 2016). Section 3.2.4.1 discusses the inorganic dissolution module, while Section 3.2.4.2 discusses the additional tracers used in GMV4-nitrate.
3.2.4.1 The inorganic dissolution module
The dissolution of semi-volatile inorganic gases into the aerosol-liquid-phase has an important influence on the composition of atmospheric aerosols, as the composition of inorganic atmospheric aerosol particles is subject to exchange with the gas-phase. Variations in particle size and hygroscopicity influenced by dissolution affect radiation (ari) and aerosol-cloud (aci) interactions (described in Section 2.1.2), which in turn influence atmospheric circulation and the water cycle (Benduhn et al., 2016).
Dissolution is the combination of condensation and particle dissociation to and from the aerosol phase. Sulfuric acid (H2SO4) condenses irreversibly under tropospheric conditions, whereas semi-volatile species (such as H2O, HNO3, HCl and NH3) may re-evaporate from the aerosol phase as a function of temperature and chemical composition of the atmosphere.
Ammonium hydroxide (NH4OH) is formed from the combination of NH3 with H2O in the aerosol liquid phase, which along with HNO3 and hydrochloric acid (HCl) dissociate in the aerosol liquid phase, with water acting as a solvent (Benduhn et al., 2016).
The dissolution module within GMV4-nitrate accounts for only the gas- and aqueous-phase equilibria for the dissolution and dissociation of the following solutes (Reaction 3.1 to Reaction 3.9) (Mann, 2015; Zhang et al., 2000):
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As such GMV4-nitrate doesn’t include the liquid-solid phase equilibria, thus doesn’t allow the formation of relevant salts at low relative humidity (Reaction 3.4 to Reaction 3.9). This means that the formation of the solid-phase salts is not calculated, but the concentrations of the associated ions are considered. In doing so the complexity of modelling the hysteresis effect, alongside deliquescence and effervescence is avoided (Mann, 2015).
Deliquescence, the hysteresis effect and effervescence are all related to particle growth due to hygroscopicity and relative humidity. The deliquescence point is a point at which aerosol particle experiences a sudden size increase due to the effect of relative humidity on aerosol growth. Aerosol growth with relative humidity occurs due to the transfer of water molecules from the gas- to solid-phase. The rate of growth due to relative humidity is neither linear nor a function of relative humidity, resulting in a sudden size increase, i.e. deliquescence point (Boucher, 2015).
The hysteresis effect describes the variations in aerosol particle size with relative humidity, which differs for increasing and decreasing relative humidities. When decreases in relative humidity occur crystallisation does not occur at the deliquescence point, but occurs when relative humidity reaches the efflorescence or crystallisation humidity, i.e. a critical value which promotes crystallisation (Boucher, 2015).
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A dissolution module is a thermodynamic model required for the treatment of gas/aerosol partitioning of semi-volatile inorganic aerosols. Complications in modelling semi-volatile aerosol compound concentrations arise due to the relationship between saturation vapour pressure, aerosol composition and temperature of the atmosphere, and aerosol size distribution (Myhre et al., 2006; Benduhn et al., 2016). The dissolution of semi-volatile gases into the aerosol phase can have opposing effects on aerosol particle size. Dissolution of NH3
within H2SO4 particles results in a decrease in water content and associated particle size, due to decreases in hygroscopicity. Chemical interactions between a dissolving acid and base (such as NH3 and HNO3), may result in an increase in particle size due to additional dissolved mass (Benduhn et al., 2016).
Here a hybrid-solver, which partitions between simulating dissolution as a dynamical or equilibrium process is applied to allow the GLOMAP-mode aerosol model to a tackle the issues surrounding numerical stability and computational expense in order to allow the simulation of semi-volatile inorganic gases in to the aerosol liquid phase.
Due to numerical instability, dissolution is usually treated as an equilibrium process. The treatment of dissolution as an equilibrium process reduces the computational expense related to treating complex differential equations relating to dissolution of inorganic aerosols and associated numerical stiffness, which requires small time steps in order compensate for large variations present until the solution curve straightens out as the system approaches stability.
For example previous approaches have adopted iterative Gibbs free energy minimisation or the iterative bisection methods (Benduhn et al., 2016; Bassett and Seinfeld, 1983).
The hybrid-solver used in GMV4-nitrate treats some size increments (modal distributions) to be in equilibrium, while others are treated dynamically. The hybrid-solver developed by Benduhn et al., (In Prep) uses new formalisations and decision criteria such as time and size dependant (modal) choices between the equilibrium and transition approach, to combine computational efficiency with an accurate representation of the dynamical properties of the processes of dissolution (Benduhn et al., 2016).
Through the development and implementation of two frameworks for both transient and equilibrium formulations for dissolution the hybrid-solver treats dissolution as a choice-wise dynamic or static process (Benduhn et al., 2016). Benduhn et al., (In Prep) have shown that the hybrid-solver achieves numerical accuracy with modest computational expense through evaluation in box model experiments under a range of atmospheric conditions. This hybrid-solver has been evaluated to be in good agreement with observed surface concentrations of
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NO3 and NH4 (in Europe, the U.S. and East Asia), capture the partitioning of HNO3 and NH3 into Aitken mode sized particle; with modest computation expense (Benduhn et al., 2016).
3.2.4.2 Gas- and aerosol-phase tracers within the nitrate-extended version of the TOMCAT-GLOMAP-mode coupled model
GMV4-nitrate has a total of 285 tracers, consisting of: 35 advected aerosol tracers; 77 gas-phase species; 164 budget terms, and; 4 water content and 5 cloud field tracers. The gas-gas-phase advected tracers in GMV4-nitrate follow the same setup as version of GLOMAP-mode described in Mann et al. (2010), but with the addition of a NH3 tracer.