Microphysics_0M

The Microphysics_0M.jl module defines a 0-moment bulk parameterization of the moisture sink due to precipitation. It offers a simplified way of removing the excess water without assuming anything about the size distributions of cloud or precipitation particles.

The $q_{tot}$ (total water specific humidity) sink due to precipitation is obtained by relaxation with a constant timescale to a state with condensate exceeding a threshold value removed. The threshold for removing excess $q_{tot}$ is defined either by the condensate specific humidity or supersaturation. The thresholds and the relaxation timescale are defined in CLIMAParameters.jl.

Note

To remove precipitation instantly, the relaxation timescale should be equal to the timestep length.

Moisture sink due to precipitation

If based on maximum condensate specific humidity, the sink is defined as:

\[\begin{equation} \left. \mathcal{S}_{q_{tot}} \right|_{precip} =- \frac{max(0, q_{liq} + q_{ice} - q_{c0})}{\tau_{precip}} \end{equation}\]

where:

$q_{liq}$, $q_{ice}$ are cloud liquid water and cloud ice specific humidities,
$q_{c0}$ is the condensate specific humidity threshold above which water is removed,
$\tau_{precip}$ is the relaxation timescale.

If based on saturation excess, the sink is defined as:

\[\begin{equation} \left. \mathcal{S}_{q_{tot}} \right|_{precip} =- \frac{max(0, q_{liq} + q_{ice} - S_{0} \, q_{vap}^{sat})}{\tau_{precip}} \end{equation}\]

where:

$q_{liq}$, $q_{ice}$ are cloud liquid water and cloud ice specific humidities,
$S_{0}$ is the supersaturation threshold above which water is removed,
$q_{vap}^{sat}$ is the saturation specific humidity,
$\tau_{precip}$ is the relaxation timescale.

Coupling to the state variables

Following the conservation equations for moisture and mass, the $\mathcal{S}_{q_{tot}}$ sink has to be multiplied by $\rho$ before adding it as one of the sink terms to both moisture and mass state variables. For the conservation equation for total energy, no additional source/sink terms $M$ are considered, and the the sink due to removing $q_{tot}$ is computed as:

\[\begin{equation} \left. \sum_{j\in\{v,l,i\}}(I_j + \Phi) \rho C(q_j \rightarrow q_p) \right|_{precip} = \left[\lambda I_l + (1 - \lambda) I_i + \Phi \right] \rho \, \left.\mathcal{S}_{q_{tot}} \right|_{precip} \end{equation}\]

where:

$\lambda$ is the liquid fraction
$I_l = c_{vl} (T - T_0)$ is the internal energy of liquid water
$I_i = c_{vi} (T - T_0) - I_{i0}$ is the internal energy of ice
$T$ is the temperature,
$T_0$ is the thermodynamic reference temperature (which is unrelated to the reference temperature used in hydrostatic reference states used in the momentum equations),
$I_{i0}$ is the specific internal energy of ice at $T_0$
$c_{vl}$ and $c_{vi}$ are the isochoric specific heats of liquid water, and ice.
$\Phi$ is the effective gravitational potential.

This assumes that the $\mathcal{S}_{q_{tot}}$ sink is partitioned between the cloud liquid water and cloud ice sinks $\mathcal{S}_{q_{liq}}$ and $\mathcal{S}_{q_{ice}}$ based on the cloud liquid water and cloud ice fractions.