Methods

Chapter IV: Size-Dependent Nitrate Particle Growth Parameterization for

4.2 Methods

parameterize this rapid nanoparticle growth based on the physics of gas-to-particle conversion. Because the thermodynamic driving force for this rapid growth is solely saturation ratio, and there is no complex organic reaction involved, the contribution of condensation on particle growth can be isolated and carefully examined. The derived parameters will be then incorporated into the Global Model of Aerosol Processes (GLOMAP, Spracklen et al., 2005). The new growth mechanism will bridge the gap between particles in nucleation mode, Aitken mode, and accumula- tion mode, which were previously in separate modules and thought to be irrelevant to one another for nitrate particles within one simulation time step. Since adding the new mechanism will reduce the vapors available for particle formation and grow particles to larger sizes, it will affect particles in all sizes. This work opens up a new perspective on describing nanoparticle growth and activation to CCNs in large-scale modeling, which may help to bring the modeling results closer to observations and reduce the uncertainty for calculating the Earth’s radiative forcing.

matsu Hg-Xe UVH lamps at wavelengths between 250 to 450 nm. Experiments were conducted in the presence of ions produced by galactic cosmic rays (GCR), at concentrations typical at sea level, or by a high-flux pion beam (3.6-GeV) to re- produce ion-pairs concentrations in the upper troposphere. Additional experiments were performed under neutral conditions by removing ions with field cage electrodes at the end of the chamber (±30𝑘𝑉).

Gas-phase sulfuric acid, nitric acid, and ammonia concentrations were monitored by a nitrate chemical ionization atmospheric pressure interface time-of-flight (CI- APi-TOF) mass spectrometer (Kürten et al., 2011), a bromide CI-APi-TOF mass spectrometer (Jokinen et al., 2012), and a water cluster CI-APi-TOF mass spec- trometer (Pfeifer et al., 2020), respectively. VOCs were measured by a proton transfer reaction time-of-flight mass spectrometer (PTR-TOF-MS Breitenlechner et al., 2017. An iodide adduct chemical ionization time-of-flight mass spectrometer equipped with a Filter Inlet for Gases and Aerosols (FIGAERO-CIMS) was em- ployed to measure particle phase composition (Lopez-Hilfiker et al., 2014). Particle size distributions were retrieved from combining measurements from a differential mobility analyzer train (DMA-train, Stolzenburg et al., 2017), a custom-built nano- Scanning Electrical Mobility Spectrometer (Kong et al., 2020), a nano-scanning mobility particle sizer (nano-SMPS, Tröstl et al., 2015), and a long-SMPS (Jurányi et al., 2011), with size ranges specified as in Wang et al. (2020).

Growth rate parameterization using aerosol dynamic equation

The continuous general aerosol dynamic equation is defined in J. Seinfeld and Pandis (2006) as:

𝜕 𝑛(𝑣 , 𝑡)

𝜕 𝑡

= 1 2

∫ ^𝑣

0

𝐾(𝑣−𝑞, 𝑞)𝑛(𝑣−𝑞, 𝑡) 𝑛(𝑞, 𝑡) d𝑞

− 𝑛(𝑣 , 𝑡)

∫ ∞ 0

𝐾(𝑞, 𝑣) 𝑛(𝑞, 𝑡) d𝑞− 𝜕

𝜕 𝑣

[𝐼(𝑣) 𝑛(𝑣 , 𝑡)]

+ 𝐽₀(𝑣 , 𝑡) 𝛿(𝑣−𝑣₀) +𝑆(𝑣 , 𝑡) −𝑅(𝑣 , 𝑡) (4.1) where 𝑣₀ is the lower limit of volume for a stable particle, 𝑛(𝑣 , 𝑡) is the particle volume distribution at time𝑡 and volume 𝑣, 𝐾(𝑞, 𝑣) is the coagulation coefficient between particle of volume 𝑣 and 𝑞, 𝐽₀ is the homogeneous nucleation rate that provides a source of particles of size𝑣₀,𝑆(𝑣 , 𝑡), 𝑅(𝑣 , 𝑡), and𝐼(𝑣 , 𝑡)are the sources, sinks, and growth of particle of volume𝑣, respectively. The time- and size-dependent condensational growth rate of aerosols within a well-defined air mass at size𝑑_pcan

then be written as:

𝜕 𝑛 𝑑_p, 𝑡

𝜕 𝑡

+ 𝜕

𝜕 𝑑_p

𝑛 𝑑_p, 𝑡

𝐼 𝑑_p, 𝑡 = 𝐽_𝜈 𝛿(𝑑_p)

+𝑆 𝑑_p, 𝑡

(4.2)

− 𝐾_𝑐 𝑑_p, 𝑡

𝑛 𝑑_p, 𝑡

− Õ

𝑖

𝑅_𝑖 𝑑_p, 𝑡

𝑛 𝑑_p, 𝑡

where𝐾_𝑐 𝑑_p, 𝑡

represents the complete coagulation kernel for particle at diameter 𝑑_𝑝. The entire equation can be solved numerically by showing that𝑑_p= 𝑑_p(𝑡)along a growth characteristic, and the rate of diameter change of a particle as a result of condensation or evaporation is then:

𝐼_d 𝑑_p, 𝑡

= d𝑑_p d𝑡

(4.3) for a particle that is neither added to the population at size 𝑑_p nor lost from that size at time𝑡. Furthermore, if we define the flux through size space as𝐹 𝑑_p(𝑡)

= 𝑛 𝑑_p(𝑡)

𝐼_𝑑 𝑑_p(𝑡)

, we can apply the method of characteristics to show that the time rate of change of𝐹along the growth path of any particle is:

d𝐹 𝑑_p(𝑡) d𝑡

= −𝑛 𝑑_p(𝑡) d𝐼_𝑑 𝑑_p(𝑡) d𝑡

+𝐽_𝜈 𝛿(𝑑_p)

+𝑆 𝑑_p𝑡

− 𝐾_c 𝑑_p, 𝑡

𝑛 𝑑_p, 𝑡

−Õ

𝑖

𝑅_𝑖 𝑑_p, 𝑡

𝑛 𝑑_p, 𝑡

(4.4) To evaluate the flux and diameter variation along a growth characteristic, we then model the gas-to-particle conversion contribution to the growth rate as:

𝐼 𝑑_p

=2𝜋 𝑑_p 𝑓 (Kn, 𝛼)

𝑁_∞−𝑁_satexp 𝑑_K

𝑑_p

(4.5) where 𝑓 (Kn, 𝛼) is the correction factor due to noncontinuum effects (Kn) and imperfect surface accommodation (𝛼), 𝑁_∞ and 𝑁_sat are vapor concentration and saturation vapor concentration, respectively, and

𝑑_K = 2𝜎 𝑀

𝑅𝑇 𝜌_p (4.6)

is the Kelvin diameter, a material property that accounts for the effect of the surface free energy of the particle on the partial pressure that is required to maintain vapor- liquid equilibrium with the droplet. 𝜎is the surface tension and𝑀is the molecular weight of the substance, and 𝜌_p is the liquid-phase density. The sinks of particles

considered in this study include dilution loss, particle wall loss, and coagulational loss. With all the instruments connected the CLOUD facility, the total sampling flow rate was 270 L min⁻¹, resulting in a dilution lifetime of 1.6 h in the 26.1 m³ chamber:

𝑅_dil=𝑘_dil𝑛(𝑑_p, 𝑡) =1.72×10⁻⁴s⁻¹𝑛(𝑑_p, 𝑡) (4.7) Particle wall lose rate was extrapolated from the sulfuric acid wall loss rate:

𝑅_wall =𝑘_wall𝑛(𝑑_p, 𝑡) =2.116×10⁻³ 𝑇

278 T

0.875 0.82

𝑑_p

𝑛(𝑑_p, 𝑡) (4.8)

The coagulation coefficient between two particles at𝑑_p,iand𝑑_p,jis defined as:

𝐾_{𝑖, 𝑗} = 2𝜋(D𝑖+ D𝑗) (𝑑_p,i+𝑑_p,j)

×

"

𝑑_p,i+𝑑_p,j 𝑑_p,i+𝑑_p,j+2(𝑔²

𝑖 +𝑔²

𝑗)^1/2 + 8(D𝑖+ D𝑗) 𝛼(𝑐¯²

𝑖 +𝑐¯²

𝑗)^1/2(𝑑_p,i+𝑑_p,j)

#

(4.9)

where D is particle diffusivity, ¯𝑐 is the particle mean velocity and 𝑔 is the mean distance from the surface of a sphere covered by a particle after moving one mean free path (FUCHS:1971aa; Charan et al., 2019):

𝑔_𝑖=

√ 2𝜋𝑐¯_𝑖 24D𝑖 𝑑_p,i

"

𝑑_p,i+8D𝑖

𝜋𝑐¯_𝑖 3

−

𝑑²

p,i+ 64D_𝑖² 𝜋²𝑐¯²

𝑖

3/2#

−𝑑_p,i (4.10) After solving the given general dynamic equation and recovering the sink-free par- ticle growth profile, the condensational flux,𝐼(𝑑_p), as defined in Eq. (4.5), and the Kelvin diameter, 𝑑_K, defined in Eq. (4.6), can be computed as the two signature parameters that will then be applied in the aerosol box model GLOMAP to represent the gas-to-particle conversion for nanoparticle growth.

Global modeling of nitric acid and ammonia with TOMCAT/GLOMAP The GLobal Model of Aerosol Processes (GLOMAP) is the aerosol microphysics module in the TOMCAT 3-D Eulerian offline chemical transport model (Spracklen et al., 2005; Mann et al., 2010). The baseline model of GLOMAP nitrate module includes all the nucleation mechanisms from previous CLOUD experiments, such as the ternary inorganic nucleation, biogenic nucleation and amines nucleation (Kirkby et al., 2011; Riccobono et al., 2014; Kirkby et al., 2016). The meteorology is forced by ERA-Interim (Berrisford et al., 2011). Climatology of biomass burning

emissions and dust are included, but there is no marine or anthropogenic organic emission. Emission data are retrieved from the AeroCom 2000 dataset (Dentener et al., 2006), including the ammonia emission data from Bouwman et al. (1997).

The nitrate solver assumes all particles are liquid or in aqueous solution, irrespective of relative humidity, temperature, or particle size. Particle sizes are represented by four different modes: nucleation (3-10 nm), Aitken (10-100 nm), accumulation (100–1000 nm), and coarse (> 1000 nm). Figure 4.1, 4.2, and 4.3 shows the annual mean concentrations at different altitudes of SO₂, NH₃ and HNO₃ respectively, using the described baseline model. Figure 4.4 demonstrates the particle number concentration predicted by the current baseline model, which already indicates an underestimation of nucleation events in the upper free troposphere as particle numbers decreases with altitudes. In addition, the current model also shows the molecular ratio of ammonium to sulfate (NH⁺₄/SO²⁻₄ ) in particle phase can be as high as 20 at the lower altitude, suggesting nitrate may be a major contributor to particles in the nucleation mode (Figure 4.5) at the surface. The seasonal variation of nitrate particulate mass fractions shown in Figure 4.6 indicates that nitrate has a great impact on particles in the nucleation mode at lower temperatures. The simulated total number concentration using the baseline GLOMAP model is generally biased low compared to the observation data from the NASA Atmospheric Tomography Campaign (Atom-1) (Wofsy et al., 2018), especially in the tropics (Figure 4.7).