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Aerosol nucleation: notation and key assumptions

Here we first introduce the notation used in the description of MAM's aerosol nucleation parameterization and introduce the key assumptions.

Mass and number mixing ration tendencies

Nucleation changes the mixing ratios of gas species as well as the mass and number mixing ratios of relevant aerosol species and modes. For the formation of particles in lognormal mode \(i\), the relationships among the tendecies are

\[ \begin{align} \left( \frac{d q_{m,L,i}}{dt} \right)_{\rm nuc} &= \frac{m_{d,L,i}}{M_{w,L}} \left(\frac{d q_{n,i}}{dt}\right)_{\rm nuc} \,, \label{eqn:aer}\\ % \left( \frac{dq_{v,L}}{dt} \right)_{\rm nuc} &= -\left(\frac{d q_{m,L,i}}{dt}\right)_{\rm nuc} \,, \label{eqn:gas} \end{align} \]

where

  • \(q_{m,L,i}\) is the aerosol mass mixing ratio of species \(L\) in mode \(i\) (unit: kmol of species \(L\) per kmol of dry air);

  • \(q_{n,i}\) is the aerosol number mixing ratio of mode \(i\) (unit: # of aerosols per kmol of dry air);

  • \(q_{v,L}\) is the mass mixing ratio of gas species \(L\) (unit: kmol of species \(L\) per kmol of dry air);

  • \(m_{d,L,i}\) is the mean dry mass of a new nucleus in mode \(i\) that contains species \(L\) (unit: kg).

  • \(M_{w,L}\) is the molecular weight of species \(L\) (unit: kg/kmol).

Assumptions

Nucleation mechanisms

Aerosol nucleation in the real atmosphere can be homogeneous or heterogenous (distinguished by the absence or presence of existing partcles) and can involve one or multiple gas species. The 4-mode configuration of MAM considers only one mechanism of nucleation, i.e., the binary nucleation involving water and sulfuric acid gas. In the planetary boundary layer (PBL), an empirical parameterization is also used in order to avoid overly weak nucleation in the PBL.

Initial growth of new particles

The sizes of the newly formed molecule clusters are typically on the order of 1 nm. The smallest aerosol particles represented by the 4-model configuration of MAM are in the Aitken mode with prescribed minimum mode mean diameter of 8.7 nm. Therefore, MAM4's nucleation parameterization considers not only the formation of small new clusers but also the initial growth of such clusters to the size of Aitken-mode particles. This initial growth is assumed to increase the particle sizes to those of the Aitken mode, and not larger. In other words, in MAM4, the subscript \(i\) in the expressions above corresponds to the index of the Aitken mode. The nucleation related mass and number mixing ratios tendencies are zero for other lognormal modes.

Physical constants

The densities (i.e., mass per unit volume of aerosol) of aerosol sulfuric acid and sulfate are assumed to be the same (i.e., \(\rm 1770~kg~m^{-3}\));

Tendencies provided to the host model

With the assumptions described above, the tendencies that MAM4 provided to the host model are

\[ \begin{align} \left(\frac{dq_{n,i}}{dt}\right)_{\rm nuc}&= \frac{10^6 J_{nuc}}{c_{air}} \,, \label{eqn:jnuc} \\ % \left(\frac{dq_{m,SO_4,i}}{dt}\right)_{\rm nuc} &= \frac{m_{d,SO_4}}{M_{m,SO_4}} \left(\frac{dq_{n,i}}{dt}\right)_{\rm nuc} \,, \label{eqn:amass} \\ % \left(\frac{dq_{v,H_2SO_4}}{dt}\right)_{\rm nuc} &= - \left(\frac{dq_{m,SO_4}}{dt}\right)_{\rm nuc} \,, \label{eqn:vmass} \end{align} \]

with \(i=2\) (i.e., the Aitken mode). Here,

  • \(J_{nuc}\) is the nucleation rate after taking into account the initial growth of new particles (unit: cm\(^{-3}\) s\(^{-1}\)),
  • \(c_{air}\) is the molar concentration of the dry air (unit: kmol of air per m\(^3\).
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