emc2.simulator.psd.calc_mu_lambda

emc2.simulator.psd.calc_mu_lambda(model, hyd_type='cl', calc_dispersion=None, dispersion_mu_bounds=(2, 15), subcolumns=False, is_conv=False, **kwargs)

This method calculated the Gamma PSD parameters following Morrison and Gettelman (2008). Note that the dispersion cacluation from MG2008 is used in all models implementing this parameterization except for ModelE and DHARMA, which use a fixed definition. Note #2: subcolumns are hardwired as True in radar_moments.py and lidar_moments.py, which means that we assume that the PSD mu and lambda definition applies to the SGS. This defintion might be under future discussion (whether to apply this assumption or not). Calculates the \(\mu\) and \(\lambda\) of the gamma PSD given \(N_{0}\). The gamma size distribution takes the form:

\[N(D) = N_{0}e^{-\lambda D}D^{\mu}\]

Where \(N_{0}\) is the intercept, \(\lambda\) is the slope, and \(\mu\) is the dispersion.

Note: this method only accepts the microphysical cloud fraction in order to maintain consistency because the PSD calculation is necessarily related only to the MG2 scheme without assumption related to the radiation logic.

Parameters:

model: :py:mod:`emc2.core.Model`

The model to generate the parameters for.

hyd_type: str

The assumed hydrometeor type. Must be a hydrometeor type in Model.

calc_dispersion: bool or None

If False, the \(\mu\) parameter will be fixed at 1/0.09 per Geoffroy et al. (2010). If True and the hydrometeor type is “cl”, then the Martin et al. (1994) method will be used to calculate \(\mu\). Otherwise, \(\mu\) is set to 0. If None (default), setting calculation parameterization based on model logic.

dispersion_mu_bounds: 2-tuple

The lower and upper bounds for the \(\mu\) parameter.

subcolumns: bool

If True, the fit parameters will be generated using the generated subcolumns (in-cloud) q and N quantities) rather than using the “raw” (grid-cell mean) output.

is_conv: bool

If True, calculate from convective properties. IF false, do stratiform.

Returns:

model: emc2.core.Model

The Model with the \(\lambda\) and \(\mu\) parameters added.

References

Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution: J. Climate Appl. Meteor., 22, 1764-1775

Martin, G.M., D.W. Johnson, and A. Spice, 1994: The Measurement and Parameterization of Effective Radius of Droplets in Warm Stratocumulus Clouds. J. Atmos. Sci., 51, 1823–1842, https://doi.org/10.1175/1520-0469(1994)051<1823:TMAPOE>2.0.CO;2