parcel_model.thermo.Seq¶

parcel_model.thermo.Seq(r, r_dry, T, kappa, neg=False, approx=False)¶

kappa-Kohler theory equilibrium saturation over aerosol.

Calculates the equilibrium supersaturation (relative to 100% RH) over an aerosol particle of given dry/wet radius and of specified hygroscopicity bathed in gas at a particular temperature

Following the technique of [PK2007], classical Kohler theory can be modified to account for the hygroscopicity of an aerosol particle using a single parameter, \(\kappa\). The modified theory predicts that the supersaturation with respect to a given aerosol particle is,

\[\begin{split}S_\text{eq} &= a_w \exp \left( \frac{2\sigma_{w} M_w}{RT\rho_w r} \right)\\ a_w &= \left(1 + \kappa\left(\frac{r_d}{r}^3\right) \right)^{-1}\end{split}\]

with the relevant thermodynamic properties of water defined elsewhere in this module, \(r_d\) is the particle dry radius (r_dry), \(r\) is the radius of the droplet containing the particle (r), \(T\) is the temperature of the environment (T), and \(\kappa\) is the hygroscopicity parameter of the particle (kappa).

This method has been extended to supply the negative of the supersaturation if specified using the argument neg; this is useful when attempting to numerically estimate the particle’s critical radius, as done in kohler_crit(). Otherwise, this method will return the supersaturation as a decimal with respect to 1.0,

\[S_\text{eq} = S - 1.0\]

Additionally, passing the argument approx will return instead the canonical approximation to the Kohler equation,

\[S_\text{eq} = \frac{2\sigma_{w} M_w}{RT\rho_w r} - \kappa\frac{r_d^3}{r^3}\]

which is valid when the equilibrium supersaturation is small, i.e. in most terrestrial atmosphere applications.

Parameters:

r : float

droplet radius, m

r_dry : float

dry particle radius, m

T : float

ambient air temperature, K

kappa: float

particle hygroscopicity parameter

neg : boolean, optional (default=False)

if true, return the negative of the calculation

approx : boolean, optional (default=False)

if true, return the equilibrum supersaturation using the approximation form

Returns:

float

\(S_\text{eq}\) for the given aerosol/droplet system